•Measurements • Conversions • Units Ordinary numbers not a problem Science has very, very big numbers and very, very tiny numbers 93,000,000 Scientific notation allows the use of.
Download ReportTranscript •Measurements • Conversions • Units Ordinary numbers not a problem Science has very, very big numbers and very, very tiny numbers 93,000,000 Scientific notation allows the use of.
Slide 1
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 2
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 3
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 4
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 5
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 6
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 7
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 8
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 9
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 10
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 11
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 12
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 13
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 14
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 15
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 16
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 17
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 18
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 19
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 20
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 21
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 2
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 3
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 4
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 5
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 6
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 7
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 8
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 9
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 10
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 11
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 12
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 13
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 14
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 15
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 16
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 17
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 18
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 19
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 20
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21
Slide 21
•Measurements
• Conversions
• Units
1
Ordinary numbers not a problem
Science has very, very big numbers and very,
very tiny numbers
93,000,000
Scientific notation allows the use
of ordinary
Miles
Away
numbers with a scientific notation that
expands our range of describing numbers,
both large and small numbers.
.000,000,0015
6
93x10 miles
2
10 raised to an exponent gives us the option
of very big and very tiny numbers.
For big numbers, the exponent is (+ )and for
tiny numbers it is (-).
This tells us how many decimal places are
taken up by the exponent
347,000
Another method is to use text
to
describe
a
347,000
number.
347x103
347 kilo (spoken)
347 k (written)
3
101 = 10 = ten: add 1 place
102 = 100 = one-hundred: add 2
103 = 1000 = one-thousand: add 3
104 = 10,000 = ten-thousand: add 4
A number of 5.36(000) x 105 is 536,000
Five (5) decimal places moved to the right is
the same number as the exponent
4
Try this:
What is the number:
8.57 x 104 = ?
What in exponent form is:
9,000,000,000 =?
5
What is the number: 8.57 x 104 = ?
Answer: 85,700 : move decimal 4 places to
the right
What in exponent form is:
9,000,000,000 =?
Answer: The 9 decimals are replaced by the
exponent: 9x109
6
Kilo = 1 thousand, multiply by 1000 which is
103.
Mega = 1 million, multiply by 1,000,000 or 106.
7
The number 54,700 calories is how many
kilocalories?
Answer: 54.7 kilo calories: 3 places
▪ Also, 54.7x103 cal
The number 5,470,000 joules is how many
megajoules?
Answer: 5.47 megajoules : 6 places
▪ Also, 5.47x 106 cal
8
Number
Exponent format
Text format
5688 cal
5.688x103 cal
5.688 kilocal
5.688 kcal
5.688x103 cal
5688 cal
934,000 J
.934x106 J
.934 MegaJoule
28,800,000 J
28.8x106 J
28.8 Megajoule
1000
103
kilo
1000000
106
mega
9
.00000000015
Small numbers needed to describe atomic
level parameters, and phenomena, ex. waves,
light
Atomic diameters approximately
10-10 m, nucleus is about 10-15 m
Meter stick smallest
dimension is a millimeter,
.001m, or 10-3 m
Wavelength of red light is about
650 nm, nano meters, 650x10-9 m
1500 waves in 1mm
10
Minus exponent: 10-6
Exponent is -6, which means move the
decimal 6 places to the left when
converting to the actual number, or to
the right when converting to a negative
exponent.
Example: .00347 m is 3.47x10-3 m or 3.47
millimeters (text based)
.00000347 m is 3.47x10-6 m or 3.47
micrometers
11
Number
Exponent format
Text format
.005688 m
5.688x10-3 m
5.688 millimeters (mm)
.0000000000667
6.67x10-11
667 nm
.001
10-3
milli
.01
10-2
centi
.000001
10-6
micro
.000000001
10-9
nano
12
10a x10b x10c
N
10d
N 10a+b+c-d
If
104 x106 x103
4 6 3( 33)
5
N
10
10
(103 )2
Sample
4.46 x104 x 6.22 x106 x 9.88 x103
3
N
but
,.00247
is
just
2.47
x
10
(.00247)2
Gathering coefficient and breaking out these exponents part of the
problem, this becomes:
4.46 x6.22x9.88
5
5
N
x
10
44.93
x
10
2.472
13
Let's say, there exists a submarine at a depth of 400 m, what is the pressure on
the sub's surface at that depth?
Solution: P Dgh,N/m2
We know that g 9.8m/s2 and that density of sea water is 1030kg/m3
First, convert to exponent format to simplify:
Thus, gremains g 9.8m/s2 and D 1.030 103 and h 4.00 102
P 1.030 103 9.8 4.00 102
P 1.030 9.8 4.00 1032 40.38 105 N/m2
14
34000 is 2 significant figures
3.4000 is 2 significant figures
.3400 is 2 significant figures
.00340 is 2 significant figure
34100 is 3 significant figures
34107 is 5 significant figures
.0000000341 is 3 significant figures
15
Let’s say you have measured the diameter of a
right circular cylinder and it is 2.45 cm. You
want to know the area.
π= 3.14
A= π r2 = 3.14x.012252 = .000471196 m2
Why not report this number instead of a 3
significant figure answer of .000471 ?
16
A rod measures 5.54 cm. Convert this to m.
Answer: .0554 m
Some powder has a mass of
34.8 mg convert this to grams and also kg.
Answer .0348 grams
Answer .0000348 kg
17
You may convert units from to MKS and vice
versa.
Many measurements are made in English
units, and must be converted to MKS to use
the formulas properly.
18
Convert miles/hour to meter/second (m/s)
miles 1 1 m
x x
hour 1 1 s
miles 1609 m 1 hour miles
m
x
x
x.447
hour 1 mile 3600 s hour
s
19
A car is moving at 35 miles per hour, and speeds
up to 52 miles per hour. What is the increase in
m/s ?
35miles/hr x .447 m/s/ mile/hour = 15.65 m/s
and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s.
Thus, the increase is:
23.24 -15.65 = 7.594 m/s
20
1000 g= 1 Kilogram
1 Mile=5280 feet
1 gram = .001 kg
1 N = .225 lbs
1 m = 3.28 feet
1 lb = 4.45 N
1 mile = 1609 m
1 hour = 3600 s
1 cm =.01 m
1 minute = 60 s
1 mm = .001 m
1 day = 24 hours
1 m/s = 2.24 miles/hr
1 miles/hour = .447 m/s
21