Lecture 2 Fall 2007. Units of
measurement. Sections 1.4
through 1.6.
1.4. Units of Measurement.
Must have units – SI units are
the Systeme International. This
has 7 base units from which all
other units are derived:
The 7 base units from which all
other units are derived:
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Physical
Unit
abbreviation
Quantity_______________________
Mass
kilogram
kg
Length
Meter
m
Time
second
s or sec
Temperature Kelvin
K
Amount of
Substance
Mole
mol
Prefixes are used to indicate decimal
fractions or multiples of the above units:
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Prefix
Giga
Mega
Kilo
Deci
Centi
Milli
Micro
Nano
Pico
Femto
Abbr. meaning
G
109
M
106
k
103
d
10-1
c
10-2
m
10-3
μ
10-6
n
10-9
p
10-12
f
10-15
example
gigameter
megameter
1 kilometer
1 deciliter
1 centiliter
1 milligram
1 microgram
1 nanometer
1 picogram
1 femtosecond
Derived SI units:
• Volume: The volume of a cube is given by the
lengths of its sides multiplied together. Thus,
the volume of anything has the units m3, or
cm3. The most commonly used unit of
volume in chemistry is the liter, which is a
dm3. 1 mL = 1 cm3 is interchangeable.
a
b c
Volume = a x b x c
Units = meters x meters x meters
= m3
or
= cm x cm x cm
= cm3 or ml or cc
Density:
• Density is mass/volume. Commonly
expressed as gm/ml or gm/cc.
• Densities of some common
substances:
• __________________________________
• Air
0.0001 g/cc Ethanol: 0.79
• Water: 1.00
Table salt: 2.16
• Iron: 7.9
Gold:
19.32
1.5. Uncertainty in Measurement:
• Exact numbers: e.g. number of inches in a
foot, number of people in the lecture theater.
Are usually defined numbers.
• Inexact Numbers: These are measured
numbers, which always have a degree of
uncertainty. Suppose ten students measure
the mass of the same dime on ten different
balances. They will all get slightly different
values. (=2.2811 g. a quarter weighs 5.57 g))
Precision and accuracy:
Precision is how closely a set of
measurements agree with each other.
Accuracy is how closely the set of
measurements agree with the correct
or true value.
good accuracy
good precision
Significant Figures:
Suppose you measure the weight of a
dime on a balance stated to be accurate
to 0.0001 g. You could report the weight
as 2.2405 ± 0.0001 g.
Measured quantities are reported in
such a way that only the last digit is
uncertain.
All digits of a measured quantity are
called significant figures.
To determine the number of significant
figures in a number start counting digits
from the left to the right.
Note: Zeroes at the end or in the middle
of a number are significant, those at the
beginning are not.
0.000103
three significant figures
1.030
four “
“
1.0300 x 105
five “
“
Significant Figures in
Calculations:
For multiplication and division: The
result contains the same number of
significant figures as the measurement
with the fewest significant figures:
e.g. area = 6.221cm x 5.2 cm = 32.3492 =
32 cm2.
Only two significant
figures
Addition and Subtraction.
For addition and subtraction: The result
contains the same number of decimal
places as the result with the fewest
decimal places.
e.g. 20.42 + 1.322 + 83.1 = 104.842 = 104.8
Dimensional Analysis
Converting inches into cm:
Conversion factor: same quantity
but in different units
2.54cm
23.2in 
 58.9cm
1in
the units to be eliminated go on
opposite sides of the fraction
Dimensional Analysis
Converting m/min into m/s:
Conversion factor
m
1 min
m
1.2
×
= 0.020
min
60 s
s
the units to be eliminated go on
opposite sides of the fraction
Dimensional Analysis
More than one conversion:
A car travels 12 km per liter of gasoline.
How many many miles per gallon will it
go?
=>
Convert 12 km/L into mi/gallon
=>
first, convert length units: km into mi,
second, convert volume units: L into gallons
Dimensional Analysis
km
12
×
L
1 mi
1.61 km
?
or
1.61 km
1 mi
?
Dimensional Analysis
km
1 mi
mi
12
×
= 7.45
1.61 km
L
L
Place conversion factor
so units to be removed
will cancel
Dimensional Analysis
3.785 L
mi
mi
7.45
×
=
28.198
L
1 gal
gal
mi
= 28
gal
Note: 12 kilometers has only two significant figures,
so answer must have only two significant figures
Conversions involving squared
and cubic units:
The volume of a container is 5.3 m3.
What is the volume in cm3?
Convert m3 into cm3
Conversion factor =
100 cm
1 meter

Vol in cm3 = 5.7 meter3 x
= 5,700,000 cm3
or
100 cm
1m
100 cm x 100 cm x 100 cm
1 meter
1 meter 1 meter
(note: 1 m3 = 1 m x 1 m x 1 m)