Transcript Slide 1

Metric System
of
Measurement
What is the metric system?
Why do we have to learn this?
• Standard: 8Sa: you will demonstrate an understanding of
technological design and scientific inquiry, including process
skills, mathematical thinking, controlled investigative design
and analysis, and problem solving.
• Objectives:
– You will convert, apply, and arrange metric conversion units
– You will use, apply, and evaluate metric prefixes, and base units to labs
– You will apply unit factor analysis, scientific notation, and significant
figures to metric calculations.
– You will apply the ladder method and division and multiplication by 10 to
calculate and convert metric units.
The Metric system of measurement
was created about two hundred years
ago by a group of French scientists to
simplify measurement.
Math and Units
• Math- the language of Science
• SI Units – International System
• Meter
m
• Mass
g
• Time
s
• Volume
L
• Temperature oC, Kelvin K
Length:
• The measured • Base unit in
distance from
the metric
one end to the system is the
other of an
object.
Meter (m)
1 meter (1m)
1 meter (1m)
or the length of a baseball bat
1 millimeter (1 mm)
About the thickness of a dime
1 centimeter (1 cm)
1 kilometer (1 km)
OR About the length of 10 football fields
Mass:
• A quantity of
matter.
• Base unit in
the metric
system is the
Gram.
1 gram (1 g)
or the mass
of a
paperclip
1 milligram (1 mg)
About the mass of a grain of sand
1 kilogram (1 kg)
Volume / Capacity
• Space
included
within limits
as measured
• Base unit in
the metric
system is the
Liter.
1 liter (1 L)
1 liter of coke
1 liter (1 L)
1 milliliter (1 mL or 1 ml)
Capacity of an eyedropper
1 kiloliter (1kL or 1 kl)
About the
capacity of
4 bathtubs
Temperature:
• The degree of • Base unit in
hotness or
the metric
coldness of
system is the
something
Celsius.
Temperature
A measure of how hot or how cold an
object is.
SI unit: Celsius or Centigrade (old term)
SI Unit: the kelvin
(K)
• Note: not a degree
• Absolute Zero= 0 K
degree Celsius (°C)
Convert Temperatures
Formulas
• °C x 9/5 + 32 = °F
or
• °C = (°F -32)/1.8
• (°F - 32) x 5/9 = °C
or
• °F = (°C x 1.8) + 32
Fahrenheit Formula
180°F
100°C
=
Zero point:
9°F
5°C
=
1.8°F
1°C
0°C = 32°F
°F
= 9/5 T°C + 32
°F
= 1.8 T°C + 32
or
24
Celsius Formula
Rearrange to find T°C
°F
=
1.8 T°C + 32
°F - 32
=
1.8T°C ( +32 - 32)
°F - 32
=
1.8 T°C
1.8
°F - 32
1.8
=
T°C
1.8
25
Temperature Conversions
A person with hypothermia has a body
temperature of 29.1°C. What is the body
temperature in °F?
°F =
1.8 (29.1°C) + 32
exact
tenth's
=
52.4 + 32
=
84.4°F
exact
tenth’s
26
Learning Check
Pizza is baked at 455°F. What is that in °C?
1) 437 °C
2) 235°C
3) 221°C
27
Solution
Pizza is baked at 455°F. What is that in °C?
2) 235°C
(455 - 32) = 235°C
1.8
28
Learning Check
On a cold winter day, the temperature
falls to -15°C. What is that temperature
in °F?
1) 19 °F
2) 59°F
3) 5°F
29
Solution
3) 5°F
Solution:
°F = 1.8(-15°C) + 32
= -27 + 32
= 5°F
30
A long time ago in a faraway galaxy and in
a deluxe castle, there lived a monarch who
loved chocolate milk.
His name was
Henry, and he
was known to all
of his subjects as,
King Henry
Throughout his kingdom, King Henry made
sure that all of the cows were fed great
supplies of chocolate to continue to provide
him with his beloved chocolate milk drink.
He had very happy cows!
King Henry drank chocolate milk with
his breakfast, lunch, and dinner.
He even drank chocolate milk for his
bedtime snack.
King Henry drank chocolate milk by
the liter!
King Henry wanted all living
creatures in his kingdom to
enjoy chocolate milk as much
as he enjoyed chocolate milk.
However, a liter was not the best
serving size for every creature.
The Royal Potter was called for and the
command was given for new serving vessels
to be created to fit every creature in the
kingdom.
For the creatures smaller than
the king, the Royal Potter
designed
deciliters that were 1/10th the
size of a liter,
centiliters that were 1/100th the
size of a liter, and
milliliters that were 1/1000th the
size of a liter.
The milliliters were just right for the Royal
Chocolate Beetles found in the kingdom.
For the creatures greater than the
king, the Royal Potter designed,
Dekaliters that were 10 times the
size of a liter,
Hectoliters that were 100 times
the size of a liter, and
Kiloliters that were 1000 times
the size of a liter.
The kiloliters were just right for the
Royal Elephants of the kingdom.
The Royal Potter lined the vessels up
in his workroom from largest to
smallest to show the king.
The king’s vessel was in the center of
the line, for the king was the center of
the kingdom. The vessels were
arranged in the following order:
kiloliter hectoliter dekaliter Liter deciliter centiliter milliliter
King Henry loved the new vessels that were
designed larger and smaller than his own for all of
the living creatures in his kingdom.
The Royal Potter explained that the sizes of the
original unit of measurement increased and
decreased from the king’s liter by multiples of ten.
He explained how to convert between the sizes by
multiplying by ten or dividing by ten. King
Henry wondered how he would ever remember the
order of the vessels.
The Royal Potter said that he remembered them
by thinking of a saying. He said, “I remember the
order by saying ‘King Henry Does Usually Drink
Chocolate Milk’ and then I have no problem
remembering the order.”
“That is exactly right!” said King Henry. “Now I
shall remember the sizes of the vessels!”
He took another big drink of chocolate milk and …
died
Now it is known as the
Metric Conversion Mnemonic
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King
Henry
Died
Unexpectedly
Drinking
Chocolate
Milk
(kilo, 1,000 units)
(hecto, 100 units)
(deka, 10 units)
(Unit (liter, meter, gram, Celsius)
(deci 1/10 of a unit)
(centi 1/100 of a unit)
(milli, 1/1,000 of a unit)
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(K)ing
(H)enry
(D)ied
(W)hile
(D)rinking
(C)hocolate
(M)ilk
Copyright © 2010 Ryan P. Murphy
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(K)ing
(H)ector
(D)ied
(W)hile
(D)rinking
(C)hocolate
(M)ilk
Copyright
© 2010
Ryan
P. Murphy
Copyright
© 2010
Ryan
P. Murphy
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(K)ing
(H)ector
(D)ied
(W)hile
(D)rinking
(C)hocolate
(M)ilk
Copyright © 2010 Ryan P. Murphy
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(K)ing
(H)ector
(D)ied
(W)hile
(D)rinking
(C)hocolate
(M)ilk
Copyright © 2010 Ryan P. Murphy
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(K)ing
(H)ector
(D)ied
(W)hile
(D)rinking
(C)hocolate
(M)ilk
Copyright © 2010 Ryan P. Murphy
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•
•
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(K)ing
(H)ector
(D)ied
(W)hile
(D)rinking
(C)hocolate
(M)ilk
Copyright © 2010 Ryan P. Murphy
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(K)ing
(H)ector
(D)ied
(U)nexpectedlyhile
(D)rinking
(C)hocolate
(M)ilk
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
Copyright © 2010 Ryan P. Murphy
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King Kilometer
Hector Hectometer
Died Decameter
Unexpectedly Unit (gram, Liter, meter)
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
Copyright © 2010 Ryan P. Murphy
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King Kilometer
Hector Hectometer
Died Decameter
Unexpectedly Unit (gram, Liter, meter)
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
Copyright © 2010 Ryan P. Murphy
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King Kilometer
Hector Hectometer
Died Decameter
Unexpectedly Unit (gram, Liter, meter)
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
Copyright © 2010 Ryan P. Murphy
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King Kilometer
Hector Hectometer
Died Decameter
Unexpectedly Unit (gram, Liter, meter)
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
Copyright
© 2010
Ryan
P. Murphy
Copyright
© 2010
Ryan
P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
10-1
10-2
10-3
Copyright
© 2010
Ryan
P. Murphy
Copyright
© 2010
Ryan
P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
• King • Hector • Died -
Kilometer
Hectometer
Decameter
• Unexpectedly Unit
• Drinking Decimeter
• Chocolate - Centimeter
• Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
• King • Hector• Died •
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•
•
Kilometer
Hectometer
Decameter
Unexpectedly - Unit
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
• King • Hector• Died •
•
•
•
Kilometer
Hectometer
Decameter
Unexpectedly - Unit
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
• King • Hector• Died •
•
•
•
Kilometer
Hectometer
Decameter
Unexpectedly - Unit
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
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King Kilometer
HectorHectometer
Died Decameter
Unexpectedly Unit
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
King Henry’s Ladder
• Make a Metric Ladder in your notebook.
Metric Ladder
“Use it and you will never get lost!”
Kilo
Hecto
Deka
UNITS
deci
centi
UNITS
UNITS
UNITS
Gram
UNITS
UNITS
milli
UNITS
1000
100
10
Liter
0.1
0.01
0.001
Meter
Unexpectedly - Unit
How1m
To Use Your
100Ladder
1)
2)
Start at the unit/prefix given to you (starting point).
Count the number of steps/places to the unit/prefix
you want (final destination).
3) Move the decimal point the number of steps/places in
the same direction.
Ladder Method
1
2
KILO
1000
Units
3
HECTO
100
Units
DEKA
10
Units
DECI
0.1
Unit
Meters
Liters
Grams
How do you use the “ladder” method?
1st – Determine your starting point.
2nd – Count the “jumps” to your ending point.
3rd – Move the decimal the same number of jumps in
the same direction and add zeros for each jump
CENTI
0.01
Unit
MILLI
0.001
Unit
4 km = _________ m
Starting Point
Ending Point
How many jumps does it take?
__ __ __
4.1 .2 3. . = 4000 m
Multiplying/Dividing
Practice Problem 1
How many mg are in 3.6 Kg?
3.6 kg
Kilo
36.0
hectogram
Hecto
360. 0
dekagrams
Deka
3600. 0
grams
Gram
36000. 0 360000.0
decigrams
deci
Starting point
centigrams
centi
3600000.0
milligrams
milli
Final Destination
3,600,000 mg
6 places to the right of the decimal point
Practice Problem 2
How many hm are in 12.67 mm?
Kilo
Hecto
Deka
Meter
deci
centi
Final Destination
0.0001267 hm
5 places to the left of the decimal point
milli
Starting point
Helpful Mnemonic
King
Henry
Died
Usually
drinking
chocolate
Kay
Hollered
Dog
ARF!
dog
can’t
move
UNITS
UNITS
UNITS
UNITS
UNITS
0.1
0.01
0.001
UNITS
1000
100
10
Gram
Liter
Meter
Try to create your own mnemonic to help you
remember the prefixes and their order. This
will be important because you will not receive
the metric map on your quiz.
milk
Please convert 12.36 kg to centigrams
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King Hector Died While Drinking Chocolate Milk -
Kilogram
1000m
Hectogram
100m
Decagram
10m
Standard/Base 1m
Decigram
.1m
Centigram
.01m
Milligram
.001m
103
102
101
100
10
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 12.36 kg to centigrams
12.36
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King Hector - 1
2
Died 3
While Drinking - 4
Chocolate -5
Milk -
Kilograms
Hectograms
Decagrams
Standard
Decigrams
Centigrams
Milligrams
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 12.36 kg to centigrams
12.36
5
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King Hector - 1
2
Died 3
While Drinking - 4
Chocolate -5
Milk -
Kilograms
Hectograms
Decagrams
Standard
Decigrams
Centigrams
Milligrams
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 12.36 kg to centigrams
1236000.cm
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King Hector - 1
2
Died 3
While Drinking - 4
Chocolate -5
Milk -
Kilograms
Hectograms
Decagrams
Standard
Decigrams
Centigrams
Milligrams
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 12.36 kg to centigrams
1,236,000.cm
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King Hector - 1
2
Died 3
While Drinking - 4
Chocolate -5
Milk -
Kilograms
Hectograms
Decagrams
Standard
Decigrams
Centigrams
Milligrams
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 450 mm to hectometers
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King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 450 mm to hectometers
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•
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King Hector - 5
Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 450 mm to hectometers
.000450.0
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•
5
King Kilometer
Hector - 5 Hectometer
Died Decameter
While Standard
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 450 mm to hectometers
.00450
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5
King Kilometer
Hector - 5 Hectometer
Died Decameter
While Standard
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 450 mm to hectometers
.00450 h
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•
5
King Kilometer
Hector - 5 Hectometer
Died Decameter
While Standard
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 450 mm to hectometers
.00450 h
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•
5
King Kilometer
Hector - 5 Hectometer
Died Decameter
While Standard
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 43 cm to Decameters
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King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 43 cm to Decameters
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King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 43 cm to Decameters
43.0
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King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 43 cm to Decameters
43.0
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•
King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 43 cm to Decameters
43.0
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•
3
King Kilometer
Hector - 5 Hectometer
Died Decameter
While Standard
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 43 cm to Decameters
.043
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•
3
King Kilometer
Hector - 5 Hectometer
Died Decameter
While Standard
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 43 cm to Decameters
.043 d
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3
King Kilometer
Hector - 5 Hectometer
Died Decameter
While Standard
Drinking Decimeter
Chocolate - Centimeter
Milk Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 5241 h to mm
00000.
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King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 5241 h to mm
.
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•
King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 5241 h to mm
.
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King Hector - 5
Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 5241 h to mm
5241.00000.
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•
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5
King Hector - 5
Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 5241 h to mm
5241 00000. mm
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•
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•
5
King Hector - 5
Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 5241 h to mm
524,100,000. mm
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5
King Hector - 5
Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 9.9 m to cm
cm
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•
King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 9.9 m to cm
Answer: 990 cm
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King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 1351 Decimeters to cm
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King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 1351 Decimeters to cm
Answer: 13,510 cm
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King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 12 mm to km
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•
King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 12 mm to km
Answer: .000012 km
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•
King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 5 m to decimeters
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•
King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 5 m to decimeters
Answer: 50
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•
King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Please convert 1.3 x 104 m to centimeters
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•
King Hector Died While Drinking Chocolate Milk -
Kilometer
Hectometer
Decameter
Standard
Decimeter
Centimeter
Millimeter
1000m
100m
10m
1m
.1m
.01m
.001m
103
102
101
100
10-1
10-2
10-3
Copyright © 2010 Ryan P. Murphy
Limits of Measurement
• Accuracy and Precision
• Accuracy - a measure of how
close a measurement is to the
true value of the quantity being
measured.
Example: Accuracy
• Who is more accurate when
measuring a book that has a true
length of 17.0cm?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
• Precision – a measure of how
close a series of measurements
are to one another. A measure of
how exact a measurement is.
Example: Precision
Who is more precise when measuring
the same 17.0cm book?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm
Example: Evaluate whether the
following are precise, accurate or
both.
Accurate
Not Accurate Accurate
Not Precise Precise
Precise
Introduction to Significant Figures
&
Scientific Notation
The same rules apply with all
instruments
• The same rules apply
• Read to the last digit that you know
• Estimate the final digit
Rules for Significant figures
Rule #1
• All non zero digits are ALWAYS significant
• How many significant digits are in the
following numbers?
274
_____________
25.632
_____________
8.987
_____________
Rule #2
• All zeros between significant digits are
ALWAYS significant
• How many significant digits are in the
following numbers?
504
_____________
60002
_____________
9.077
_____________
Rule #3
• All FINAL zeros to the right of the decimal
ARE significant
• How many significant digits are in the
following numbers?
32.0
_____________
19.000
_____________
105.0020
_____________
Rule #4
• All zeros that act as place holders are
NOT significant
• Another way to say this is: zeros are only
significant if they are between significant
digits OR are the very final thing at the end
of a decimal
Significant Figures
• Scientist use _______________ to
determine how _______________ a
measurement is.
• Significant digits in a measurement include
all of the _______________ plus one
_______________ .
Rule #5
• All counting numbers and constants have
an infinite number of significant digits
• For example:
1 hour = 60 minutes
12 inches = 1 foot
24 hours = 1 day
There are 30 students in the class
For example…
• Look at the ruler below
• What would be the measurement in the
correct number of sig figs?
• _______________
Let’s try this one
• Look at the ruler below
• What would be the measurement in the
correct number of sig figs?
• _______________
Let’s try graduated cylinders
• Look at the graduated cylinder below
• What would be the measurement in the correct
number of sig figs?
• _______________
One more graduated cylinder
• Look at the cylinder below…
• What would be the measurement in the
correct number of sig figs?
• _______________
For example
How many significant digits are in the following numbers?
1)
2)
3)
4)
5)
0.0002
6.02 x 1023
100.000
150000
800
1)
2)
3)
4)
5)
_____________
_____________
_____________
_____________
_____________
How many significant digits are
in the following numbers?
1)
2)
3)
4)
5)
6)
7)
0.0073
100.020
2500
7.90 x 10-3
670.0
0.00001
18.84
1)
2)
3)
4)
5)
6)
7)
_____________
_____________
_____________
_____________
_____________
_____________
_____________
Rules Rounding Significant Digits
Rule #1
• If the digit to the immediate right of the
last significant digit is less that 5, do not
round up the last significant digit.
• For example, let’s say you have the
number 43.82 and you want 3
significant digits
Rounding Rule #2
• If the digit to the immediate right of the last
significant digit is greater that a 5, you round up
the last significant figure
• Let’s say you have the number 234.87 and you
want 4 significant digits
Rounding Rule #3
• If the number to the immediate right of the last
significant is a 5, and that 5 is followed by a non
zero digit, round up
• 78.657
(you want 3 significant digits)
Rounding Rule #4
• If the number to the immediate right of the last
significant is a 5, and that 5 is followed by a
zero, you look at the last significant digit and
make it even.
• 2.5350
(want 3 significant digits)
Say you have this number
• 2.5250
(want 3 significant digits)
Let’s try these examples…
200.99
(want 3 SF)
_____________
18.22
(want 2 SF)
_____________
135.50
(want 3 SF)
_____________
0.00299
(want 1 SF)
98.59
(want 2 SF)
_____________
_____________
How wide is our universe?
210,000,000,000,000,000,000,000
miles
(22 zeros)
This number is written in decimal
notation. When numbers get this
large, it is easier to write them in
scientific notation.
Scientific Notation
A number is expressed in
scientific notation when it is in
the form
a x 10n
where a is between 1 and 10
and n is an integer
Scientific Notation
• Scientific notation is used to express very
_____________ or very _____________
numbers
• I consists of a number between _____________
followed by _____________ to an
_____________
• The _____________ can be determined by the
number of _____________ you have to move to
get only 1 number in front of the decimal
Write the width of the universe in
scientific notation.
210,000,000,000,000,000,000,000
miles
Where is the decimal point now?
After the last zero.
Where would you put the decimal to
make this number be between 1 and
10?
Between the 2 and the 1
2.10,000,000,000,000,000,000,0
00.
How many decimal places did you move
the decimal?
23
When the original number is more than
1, the exponent is positive.
The answer in scientific notation is
2.1 x 1023
1) Express 0.0000000902 in
scientific notation.
Where would the decimal go to make the
number be between 1 and 10?
9.02
The decimal was moved how many
places?
8
When the original number is less than 1,
the exponent is negative.
9.02 x 10-8
Write 28750.9 in scientific
notation.
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•
2.87509 x 10-5
2.87509 x 10-4
2.87509 x 104
2.87509 x 105
Scientific Notation Examples
Place the following numbers in scientific notation:
1) 99.343
1) _____________
2) 4000.1
2) _____________
3) 0.000375
3) _____________
4) 0.0234
5) 94577.1
4) _____________
5) _____________
-4
10
2) Express 1.8 x
in decimal
notation.
0.00018
3) Express 4.58 x 106 in decimal
notation.
4,580,000
On the graphing calculator, scientific
notation is done with the
button.
4.58 x 106 is typed 4.58 6
6) Use a calculator to evaluate
(0.0042)(330,000).
On the calculator, the answer is
1386.
The answer in decimal notation is
1386
The answer in scientific notation
is
1.386 x 103
7) Use a calculator to evaluate
(3,600,000,000)(23).
On the calculator, the answer is:
8.28 E +10
The answer in scientific notation
is
8.28 x 10 10
The answer in decimal notation is
82,800,000,000
Write in PROPER scientific notation.
(Notice the number is not between 1 and 10)
8) 234.6 x 109
2.346 x 1011
9) 0.0642 x 104
on calculator: 642
6.42 x 10 2
Write 531.42 x 105 in scientific
notation.
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•
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•
•
.53142 x 102
5.3142 x 103
53.142 x 104
531.42 x 105
53.142 x 106
5.3142 x 107
.53142 x 108
Going from Scientific Notation to
Ordinary Notation
• You start with the number and move the
decimal the same number of spaces as
the _____________ .
• If the exponent is _____________ , the
number will be greater than 1
• If the exponent is _____________ , the
number will be less than 1
Going to Ordinary Notation
Examples
Place the following numbers in ordinary notation:
1)
2)
3)
4)
5)
3 x 106
6.26x 109
5 x 10-4
8.45 x 10-7
2.25 x 103
1)
2)
3)
4)
5)
_____________
_____________
_____________
_____________
_____________
How many Significant Figures are
there in a given measurement?
• ALIAS
»Also known as sig figs
Sig Figs
• When the decimal is present, start counting
from the left.
• When the decimal is absent, start counting
from the right.
• Zeroes encountered before a non zero digit
do not count.
How many sig figs?
100
10302.00
0.001
10302
1.0302x104
Sig Figs in Addition/Subtraction
The result has the same number of
decimal places as the number in the
operation with the least decimal
places.
Ex: 2.33 cm
+3.0 cm
5.3 cm
Sig Figs in Multiplication/Division
• The answer has the same sig figs as
the factor with the least sig figs.
• Ex: 3.22 cm
x 2.0 cm
6.4 cm2
Counting Numbers
• Counting numbers have infinite sig
figs.
• Ex: 3 apples
Base SI Units
Symbol
Quantity
Unit
Length
meter
m
Mass
kilogram
kg
Temperature
kelvin
K
Temperature
Celsius
C
Time
second
s
Derived SI Units (examples)
Quantity
unit
Symbol
Volume
cubic meter
m3
Density
Speed
kilograms per
kg/m3
cubic meter
meter per second m/s
Newton
kg m/ s2
N
Energy
Joule (kg m2/s2)
J
Units for Volume
m3
cm3
1 dm3 = 1L
dm3
1cm3= 1mL
L
mL
Liter
Unit for Weight
1 Newton
1 N= kg m/s2
Units for Energy
• Joule
• calorie
J
1 cal= 4.184 J
1 cal = quantity of heat needed to raise
the temp of 1g of water by 1 oC.
Note:
1 Cal = 1kcal =1000cal
SI Unit Prefixes
Name
gigamegakilodecicentimillimicronanopico-
Symbol
G
M
k
d
c
m
μ
n
p
109
106
103
10-1
10-2
10-3
10-6
10-9
10-12
SI Unit Prefixes for Length
Name
gigameter
megameter
kilometer
decimeter
centimeter
millimeter
micrometer
nanometer
picometer
Symbol
Gm
Mm
km
dm
cm
mm
μm
nm
pm
Analogy
109
106
103
10-1
10-2
10-3
10-6
10-9
10-12
D)
Factor Label Method of Unit
ConversionDimensional Analysis
Factor-Label Method
• Example: Convert 5km to m:
NEW UNIT
5km x 1,000m =5,000m
km
OLD UNIT
Convert 7,000m to km
7,000m x 1 km = 7 km
1,000m
Convert 2.45cs to s
• 2.45cs x 1 s
= 0.0245s
100cs
Convert 55.00 km/h to m/s
55.00 km x 1000 m x 1 h___ = 15.28m/s
h
1 km
3600 s
The End
Have Fun Measuring
and Happy Calculating!