Counting in Chemistry: Metric System
Prefixes convert the base units into units that are
appropriate for the item being measured.
Exact Numbers vs. Measurements
• Sometimes you can determine an exact value for
a quality of an object.
– Often by counting.
• Pennies in a pile.
– Sometimes by definition
• There are exactly 1000 meters in 1 kilometer.
• There exactly 2.54 cm/in
– From integer values in equations.
• In the equation for the radius of a circle (r=d/2), the 2 is
exact.
• But, whenever you use an instrument to
perform a measurement, there is uncertainty in
Significant Figures
• Measurements are written to indicate the
uncertainty in the measurement.
• The system of writing measurements we use is
called significant figures.
• When writing measurements, all the digits written
are known with certainty except the last one, which
45.872
is an estimate.
Certain
Estimated
• The estimate means we know the real value is
greater than 45.871 and less than 48.873
Estimating the Last Digit
• For instruments marked with a scale,
you get the last digit by estimating
between the marks.
52.5 mL
• Mentally divide the space into 10
equal spaces, then estimate how
many spaces over the indicator is. 100 mL graduated cylinder
• The total number of digits in a
measurement, including the last
6.31 mL
estimate are called the significant
figures or “sig figs”
• The last digit is just the best estimate
of the true value. It tells us that the 10 mL graduated cylinder
actual value is between 6.30 and
6.32 mL
Both of these measurements
have 3 sig figs
Significant Figures
• The non-placeholding digits in a
reported measurement are
called significant figures.
– Some zeros in a written number
are only there to help you locate
the decimal point.
• Significant figures tell us the
range of values to expect for
repeated measurements.
– The more significant figures there
are in a measurement, the
smaller the range of values.
Therefore, the measurement is
more precise.
12.3 cm
has 3 significant figures
and its range is
12.2 to 12.4 cm.
12.30 cm
has 4 significant figures
and its range is
12.29 to 12.31 cm.
Zeros & Significant Figures
• All non-zero digits are significant.
– 1.5 has 2 significant figures.
• Interior zeros are significant.
– 1.05 has 3 significant figures.
• Trailing zeros after a decimal point are significant.
– 1.050 has 4 significant figures.
• Leading zeros are NOT significant.
– 0.001050 has 4 significant figures
• Zeros at the end of a number without a written
decimal point are ambiguous and should be
avoided by using scientific notation.
150,000 is ambiguous
Multiplication and Division with
Significant Figures
• When multiplying or dividing measurements with
significant figures, the result has the same number
of significant figures as the measurement with the
fewest number of significant figures.
5.02 × 89,665 ×
0.10 = 45.0118 = 45
3 sig. figs.
5 sig. figs.
2 sig. figs.
2 sig. figs.
5.892 ÷ 6.10 = 0.96590 = 0.966
4 sig. figs.
3 sig. figs.
3 sig. figs.
Addition and Subtraction with
Significant Figures
• When adding or subtracting measurements with
significant figures, the result has the same
number of decimal places as the
measurement with the fewest number of
decimal places.
5.74 + 0.823 + 2.651
= 9.214 = 9.21
2 dec. pl.
4.8 1 dec. pl
3 dec. pl.
3.965 =
3 dec. pl.
3 dec. pl.
0.835 =
2 dec. pl.
0.8
1 dec. pl. (and 1 sig fig)
Multiplication/Division and
Addition/Subtraction
• When doing different kinds of operations
with measurements with significant figures,
figure out the significant figures in the
intermediate answer, then do the remaining
steps. Round only at the end for Mastering
Chemistry problems.


 n     • Follow the standard order of operations.
– Please Excuse My Dear Aunt Sally.
3.489 × (5.67 – 2.3) =
2 dp
1 dp
3.489 ×
3.37 =
12
4 sf
1 dp 2 sig figs 2 sig figs
Dimensional Analysis
• We use dimensional analysis to
convert one quantity to another.
• Most commonly dimensional
analysis utilizes conversion
factors (e.g., 1 in. = 2.54 cm)
1 in.
2.54 cm
or
2.54 cm
1 in.
• Pay attention to the units of the
answer
• Then, let the units be your guide
Dimensional Analysis
Use the form of the conversion factor that puts
the desired unit in the numerator.
Desired unit just means the next unit you need in
your calculation to get to the units needed in the
answer
Given unit 
desired unit
given unit
 desired unit
Conversion factor
© 2009, Prentice-Hall,
Inc.
Dimensional Analysis
• For example, to convert 8.00 m to inches:
• Think of the conversion steps you need:
– convert m to cm
– convert cm to in
m a solution
cm
– Draw
g map
g
in
– Put in the conversion factors so the units cancel
100 cm
1 in.
8.00
m


 315 in.
properly
1m
2.54 cm
Density as a Conversion Factor
• The gasoline in an automobile gas tank has a mass of 60.0 kg
and a density of 0.752 g/mL. What is the volume?
• Given: 60.0 kg and the density of gasoline
Solution Map:
• Find: Volume in mL
• Conversion factors:
– Density = 0.752 g/mL
– 1000 grams = 1 kg
kg
g
1000 g
1 kg
mL
1 mL
0.752 g
1000 g 1 mL
60.0 kg 

 7.98  10 4 mL
1 kg 0.752 g
For the Coming Week
• Read Chapters 1 and Chapter 2
• Work on text problems for both chapters
• Enroll in Mastering Chemistry
Mastering Chemistry Fundamentals /Chap 1 04/14/10 12:00
am
• Attendance at Lab on Thursday is required to
be able to stay in the class : Drawer check-in
and first lab.
• If your schedule changes, etc and you think
you need to drop this class, do it as soon as