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Measurements
1
Nature of Measurement
Measurement - quantitative
observation consisting of 2 parts
Part 1 - number
Part 2 - scale (unit)
Examples:
20 grams
6.63  10-34 Joule seconds
2
International System
(le Système International)
Based on metric system
and units derived from
metric system.
3
The Fundamental SI Units
4
Dimensional Analysis
or
The Unit Factor Method
Proper use of “unit factors” leads to proper
units in your answer. Unit Factor means
the ratio equals 1. Multiplying by 1
changes nothing mathematically.
Have X Wanted/Have = Wanted
Where Wanted/Have = 1 or unity
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Unit Factor Practice
1. Convert 34.5 centimeters into inches (2.54cm/1 in).
34.5 cm x 1.00 in/2.54 cm = 13.5826771653 inches
Since original measurement is good to 3 digits, we end
up with 13.6 in.
2. Convert 2376 grams into kilograms.
2376 g x 1 kg/1000g = 2.376 kg
3. Convert 14.02 Liters into gallons (3.785L/1.000 Gal).
14.02 L x 1.000 Gal/3.785 L = 3.704095 Gal
Again reduced to 4 digits so… 3.704 Gal
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Uncertainty in Measurement
A digit that must be
estimated is called
uncertain. A measurement
always has some degree
of uncertainty in the last
digit reported.
Link to exercise
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Precision and Accuracy
Accuracy refers to the
agreement of a particular
value with the true value.
Precision refers to the degree
of agreement among several
measurements of the same
quantity.
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Significant Figures - Overview
1.
2.
3.
Nonzero integers
Zeros
leading zeros
captive zeros
trailing zeros
Exact numbers
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Significant Figures - Details
Nonzero integers always count
as significant figures.
3456 has
4 sig figs.
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Significant Figures - Details
Zeros
Leading zeros do not count
as significant figures.
0.0486 has
3 sig figs.
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Significant Figures - Details
Zeros
Captive zeros always count as
significant figures.
16.07 has
4 sig figs.
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Significant Figures - Details
Zeros
Trailing zeros are significant
only if the number contains
a decimal point.
9.300 has
4 sig figs.
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Significant Figures - Details
Zeros
Trailing zeros are significant
only if the number contains
a decimal point.
9300 has
???
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Significant Figures - Details
Zeros
9300 could be 2, could
be 3, could be 4???
It is ambiguous.
Therefore, Change it to
Scientific Notation
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Significant Figures - Details
Zeros
9300
2 sig figs 9.3 X 103
3 sig figs 9.30 X 103
4 sig figs 9.300 X 103
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Significant Figures - Details
•
Exact numbers have an
infinite number of significant
figures.
1 inch = 2.54 cm
exactly
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Rules for Significant Figures
in Mathematical Operations
Multiplication and Division:
# sig figs in the result equals the
number in the least precise
measurement used in the
calculation.
6.38  2.0 =
12.76  13 (2 sig figs)
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Rules for Significant Figures
in Mathematical Operations
Addition and Subtraction: # sig figs in
the result equals the number of
decimal places in the least precise
measurement.
6.8 + 11.934 =
18.734  18.7 (3 sig figs)
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Exercise Link
Link to exercise
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Temperature
Celsius scale = C
Kelvin scale = K
Fahrenheit scale = F
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Temperature Scales
• Fahrenheit Scale, °F
– Water’s freezing point = 32°F, boiling point =
212°F
• Celsius Scale, °C
– Temperature unit larger than the Fahrenheit
– Water’s freezing point = 0°C, boiling point =
100°C
• Kelvin Scale, K
– Temperature unit same size as Celsius
– Water’s freezing point = 273 K, boiling point
= 373 K
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Temperature
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Type Unit Conversions
What if I want to convert a mass unit into a volume
unit? For example, can I convert grams into
milliliters?
g X
---------
=
mL
g
ml/g
=
mL
X
grams/milliliter is density
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Density
• Density is the mass of substance
per unit volume of the
substance:
Specific Gravity is the density of a
substance relative to the density of water
at 4 oC. This has no units!
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