The Fundamental Tools Of Science Units • Some fundamental measurements in all of science: • Length • Time • Mass • Many others are combinations of these: •
Download ReportTranscript The Fundamental Tools Of Science Units • Some fundamental measurements in all of science: • Length • Time • Mass • Many others are combinations of these: •
Slide 1
The Fundamental Tools
Of Science
Slide 2
Units
• Some fundamental measurements in all of
science:
• Length
• Time
• Mass
• Many others are combinations of these:
• Energy, Speed, Volume, Area
Slide 3
Units
• International Standard Units (SI, aka metric)
– Length (m – meter)
– Mass (kg – kilogram)
– Time (s – seconds)
– Energy (J – joules)
– Temperature (K – kelvin)
Slide 4
Temperature Scales
Boiling point
of water
Freezing point
of water
Fahrenheit
Celsius
Kelvin
212 ˚F
100 ˚C
373 K
180˚F
100˚C
32 ˚F
0 ˚C
100 K
273 K
Notice that 1 kelvin degree = 1 degree Celsius
Slide 5
Temperature
Scales
100 oF
38 oC
311 K
oF
oC
K
Slide 6
Significant Figures:
Digits in a measurement
having values that are
known with certainty plus
one digit having a value
that is estimated.
Slide 7
Reading Volume: Significant Figures on an Instrument
Slide 8
• Measurements that contain a greater
number of significant figures are more
precise than measurements that
contain fewer significant figures.
• Always select an instrument that gives
you the most significant figures. Only
report as many sig figs as that
instrument allows
Slide 9
The Rules
Slide 10
All numbers 1-9 are significant.
Zeros are sometimes significant, here's how
you can tell:
If a decimal point is present, starts on the
Pacific side, move across until you get to a 1-9
digit, and start counting to the end
1.100 has ? sig figs, 0.00540 has ?,
40.01 has ?
If a decimal point is absent, start on the
Atlantic side, move across until you get to a 19 digit, and start counting to the end
1005 contains ? sig. Figs.,
23,000 has ?,
1,045,090 has ?
Slide 11
When multiplying or dividing measurements:
round the answer to the same number of
digits as the measurement having the fewest
number of significant figures.
When adding or subtracting measurements:
round the answer to the same number of
decimal places as the measurement having
the fewest number of decimal places.
Slide 12
Higher precision
123456.7890
Lower precision
• Identify the LEAST PRECISE
measurement.
• Identify the MOST PRECISE digit (place)
within that measurement.
• Round the answer to this digit (place).
Slide 13
Conversion
• Commonly Used Prefixes:
– kilo = 1000 of something ( 1km= 1000m, kg)
– deci =0.1 of something (10 dm = 1m)
– centi = 0.01 of something (100 cm = 1m)
– milli = 0.001 of something (103 mm = 1m)
– micro = 0.000001 (106 µm = 1m)
– nano = 0.000000001 (109 nm = 1m)
– pico = 0.000000000001 (1012 pm = 1m)
Refer to Conversion Chart to additional prefixes
Slide 14
Conversion
• All conversion factors are fractions.
100 cm
1m
=
100 cm
100 cm
= 1
1 km
103
1m
10-6 µm
=
1m
10-6
µm
= 1
m
=
103 m
103
m
= 1
Slide 15
The Nature of Units
• Units are multiplied
and divided like
numbers are.
10 meters
2 meters
=5
(the units cancel out)
10 meters x 10 meters x 10 meters = 103 m3
(the units combine as exponents)
50 miles
= 5 miles/gallon (the units combine as a fraction)
10 gallons
•Only IDENTICAL UNITS
100 kg – 25 kg = 75 kg
on 2 numbers can be
added or subtracted.
•The answer always has
the same units.
100 kg – 25 m = Meaningless Dribble
Slide 16
How many seconds are in 54
days?
• Write the measurement with its unit.
• If it isn’t already a fraction, write it over 1.
• Set up conversion factors that
– Cancel units you want to get rid of
– Replace with units you are looking for
– Have values on the top and bottom that are
equivalent
• Multiply numbers across the top
• Multiply numbers across the bottom
• Divide to get answer, check units
Slide 17
Scientific Notation
• 10000000000000000000000
• 0.00000000000000000000000000001
• There has to be a better way to write those numbers
• Rules for scientific notation
– 1) Always express the number starting with the one’s place
followed by any decimal digits, times a power of 10.
– 2)To express a large number, count the number of decimal
places needed to move to the one’splace, and make that
number the exponent of ten.
– 3) To express a very small number, count the number of decimal
places needed to move to the one’s place, and make that
number the NEGATIVE exponent of ten.
– 4) After re-expressing the number in scientific notation, check it
by writing out the expanded ten, and multiply it by the measured
number.
Slide 18
Scientific Notation
•
Examples:
0.000000000000000000000000000000001
= 1.0 x 10-35
94140000000000000000000000000000000
= 9.414 x 1035
Slide 19
Slide 20
Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise
20
Slide 21
Precise if
they give
many
significant
digits
Accurate if
calibrated
to a
standard
Slide 22
To report the
accuracy of your
measurements
Observed – True
True
X 100
Slide 23
To report the
precision of your
measurements
1
Average your
measurements
2
Find the absolute values
of the differences
between each
measurement and the
average
3
Average these
differences
The Fundamental Tools
Of Science
Slide 2
Units
• Some fundamental measurements in all of
science:
• Length
• Time
• Mass
• Many others are combinations of these:
• Energy, Speed, Volume, Area
Slide 3
Units
• International Standard Units (SI, aka metric)
– Length (m – meter)
– Mass (kg – kilogram)
– Time (s – seconds)
– Energy (J – joules)
– Temperature (K – kelvin)
Slide 4
Temperature Scales
Boiling point
of water
Freezing point
of water
Fahrenheit
Celsius
Kelvin
212 ˚F
100 ˚C
373 K
180˚F
100˚C
32 ˚F
0 ˚C
100 K
273 K
Notice that 1 kelvin degree = 1 degree Celsius
Slide 5
Temperature
Scales
100 oF
38 oC
311 K
oF
oC
K
Slide 6
Significant Figures:
Digits in a measurement
having values that are
known with certainty plus
one digit having a value
that is estimated.
Slide 7
Reading Volume: Significant Figures on an Instrument
Slide 8
• Measurements that contain a greater
number of significant figures are more
precise than measurements that
contain fewer significant figures.
• Always select an instrument that gives
you the most significant figures. Only
report as many sig figs as that
instrument allows
Slide 9
The Rules
Slide 10
All numbers 1-9 are significant.
Zeros are sometimes significant, here's how
you can tell:
If a decimal point is present, starts on the
Pacific side, move across until you get to a 1-9
digit, and start counting to the end
1.100 has ? sig figs, 0.00540 has ?,
40.01 has ?
If a decimal point is absent, start on the
Atlantic side, move across until you get to a 19 digit, and start counting to the end
1005 contains ? sig. Figs.,
23,000 has ?,
1,045,090 has ?
Slide 11
When multiplying or dividing measurements:
round the answer to the same number of
digits as the measurement having the fewest
number of significant figures.
When adding or subtracting measurements:
round the answer to the same number of
decimal places as the measurement having
the fewest number of decimal places.
Slide 12
Higher precision
123456.7890
Lower precision
• Identify the LEAST PRECISE
measurement.
• Identify the MOST PRECISE digit (place)
within that measurement.
• Round the answer to this digit (place).
Slide 13
Conversion
• Commonly Used Prefixes:
– kilo = 1000 of something ( 1km= 1000m, kg)
– deci =0.1 of something (10 dm = 1m)
– centi = 0.01 of something (100 cm = 1m)
– milli = 0.001 of something (103 mm = 1m)
– micro = 0.000001 (106 µm = 1m)
– nano = 0.000000001 (109 nm = 1m)
– pico = 0.000000000001 (1012 pm = 1m)
Refer to Conversion Chart to additional prefixes
Slide 14
Conversion
• All conversion factors are fractions.
100 cm
1m
=
100 cm
100 cm
= 1
1 km
103
1m
10-6 µm
=
1m
10-6
µm
= 1
m
=
103 m
103
m
= 1
Slide 15
The Nature of Units
• Units are multiplied
and divided like
numbers are.
10 meters
2 meters
=5
(the units cancel out)
10 meters x 10 meters x 10 meters = 103 m3
(the units combine as exponents)
50 miles
= 5 miles/gallon (the units combine as a fraction)
10 gallons
•Only IDENTICAL UNITS
100 kg – 25 kg = 75 kg
on 2 numbers can be
added or subtracted.
•The answer always has
the same units.
100 kg – 25 m = Meaningless Dribble
Slide 16
How many seconds are in 54
days?
• Write the measurement with its unit.
• If it isn’t already a fraction, write it over 1.
• Set up conversion factors that
– Cancel units you want to get rid of
– Replace with units you are looking for
– Have values on the top and bottom that are
equivalent
• Multiply numbers across the top
• Multiply numbers across the bottom
• Divide to get answer, check units
Slide 17
Scientific Notation
• 10000000000000000000000
• 0.00000000000000000000000000001
• There has to be a better way to write those numbers
• Rules for scientific notation
– 1) Always express the number starting with the one’s place
followed by any decimal digits, times a power of 10.
– 2)To express a large number, count the number of decimal
places needed to move to the one’splace, and make that
number the exponent of ten.
– 3) To express a very small number, count the number of decimal
places needed to move to the one’s place, and make that
number the NEGATIVE exponent of ten.
– 4) After re-expressing the number in scientific notation, check it
by writing out the expanded ten, and multiply it by the measured
number.
Slide 18
Scientific Notation
•
Examples:
0.000000000000000000000000000000001
= 1.0 x 10-35
94140000000000000000000000000000000
= 9.414 x 1035
Slide 19
Slide 20
Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise
20
Slide 21
Precise if
they give
many
significant
digits
Accurate if
calibrated
to a
standard
Slide 22
To report the
accuracy of your
measurements
Observed – True
True
X 100
Slide 23
To report the
precision of your
measurements
1
Average your
measurements
2
Find the absolute values
of the differences
between each
measurement and the
average
3
Average these
differences