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Significant
Figures
A tutorial adapted from
www.highschoolchem.com
What are significant figures?
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Significant figures are a way of expressing
precision in measurement. In a
measurement in lab, the digits which you
can read for certain, plus one uncertain
digit, are significant.
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For instance, on the graduated
cylinder shown to the left, you will
notice that the solution is somewhere
between 25 mL and 30 mL. The first
digit is certain. We know it has to be
2. When reading a measurement,
always read the certain plus one
uncertain. Take a good guess at the
uncertain digit. Probably 8. We
would report the volume of liquid in
this graduated cylinder to be 28
mL. These would be the significant
digits. You wouldn't want to report
any more. It would be foolish to try
to get any more digits in this
answer. We just can't be sure!
If the graduated cylinder had
markings every mL instead of every 5,
we could get even more specific. You
would certainly know the first two
digits of the measurement. The
uncertain digit would be whatever you
"guess" to be the fraction of liquid to
be between the two markings.
Determining Significant Figures
in a Measurement
There are a few basic rules to remember when counting
the number of significant figures in a measurement.
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All non-zero numbers ARE significant.
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Zeros between two significant digits ARE significant.
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2051 has FOUR significant figures. Since the zero is between a
2 and a 5, it's significant.
Leading zeros are NEVER significant.
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The number 33.2 contains THREE significant figures because all
of the digits present are non-zero.
They're nothing more than "place holders". For instance, 0.54
has only TWO significant figures because the zero is leading
and a place holder. 0.0032 also has TWO significant figures.
Trailing zeros to the right of a decimal ARE
significant.

There are FOUR significant digits in 92.00 because the zeros
are trailing to the right of the decimal. Remember, they must
be there because the person measuring this value must have
been able to read these numbers from the apparatus.
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Trailing zeros in a whole number with the decimal
shown ARE significant.

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Trailing zeros in a whole number with no decimal
shown are NOT significant.

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Placing a decimal at the end of a number is usually not
done. By convention, however, this decimal will indicate a
significant zero. For instance, 540. indicates that the
(trailing) zero IS significant. There are a total of THREE
significant digits in this number.
Writing just 540 indicates that the zero is NOT significant
and there are only TWO significant figures in this value.
Exact numbers have an INFINITE number of
significant figures.

Numbers that are definitions or exact have an infinite
number of significant figures. For example1 meter = 1000
millimeters. 1 meter equals 1000.0000000... millimeters
as 1.0000000...meters equals 1000 millimeters. Both are
definitions and therefore have infinite significant figures.
Practice
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13.06 mL
0.0450 g
1.20 kg
10 lbs
10.0 seconds
1.820 L
5902.05 mg
1010.2060 g
Using significant figures in
mathematical calculations

The expression "a chain is only as strong
as its weakest link" explains why
significant figures need to be considered
when calculating. Remember, significant
figures represent the accuracy of a
measurement. When manipulating these
measurements by adding, subtracting,
multiplying, or dividing, your final answer
cannot be more accurate than the
numbers you started with. Your answer
can only be as accurate as the
measurements you start with.
Multiplication and Division
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When multiplying or dividing, count how
many significant figures are in each
measurement. Your final answer should
contain the same number of significant
figures as which ever starting value has
the least.
For example, when you take 2.045 cm X
1.3 cm, your two measurements have 4
significant figures and 2 significant
figures. Since the LEAST number of
significant figures is 2, your final answer
can only have 2 significant figures.
Addition and Subtraction
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When adding or subtracting, you must
count decimal places instead of significant
figures. Your final answer should contain
the same number of decimal places as
which ever starting value has the least.
For example, 1.994 + 16.3 = 18.294
which rounds to 18.3 using 1 decimal
place
Practice
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15.04 / 3.1
188.20 + 92.334 + 1.0008
345.04 g - 227.1 g
2.11 X 0.0006
0.891 X 200. X 13.8