Significant Figures
Chemistry 10
Significant figures: the number of digits in
an experimentally derived number that
give useful information about the data
quality
 Data with many significant figures (sig.
figs.) is considered to be precise, and
usually implies greater accuracy.
 Sig. figs. show how “good” our
instruments are to anybody looking at the
data
Accuracy: a measure of how close a measured
value is to the actual value
Precision: a measure of how reproducibly a
measurement can be taken
A paper clip’s mass is measured 3 times and the
following values are obtained: 1.0025g, 1.0026g,
and 1.0025g. What does this indicate?
If the paper clip’s actual mass is 1.9871g, the
measurements above are not ___________
because they don’t reflect the true mass.
When writing down a measurement, write all
of the digits obtained directly with the
measuring device and add a final,
estimated digit.

Example: a ruler whose smallest mark is 1
millimeter can measure lengths in 1/10 of
a millimeter.
Rules for identifying and writing Sig. Figs.
1.
2.
All nonzero digits are significant
Zeros
Leading zeros: zeros written to the left of all
nonzero digits are not significant
b. Captive zeros: zeros written between nonzero
digits are significant
c. Trailing zeros: zeros written to the right of
all nonzero digits are only significant if a
decimal point is present.
a.
3.
Scientific notation: only digits in the
portion before the “ 10n” are significant
How many significant figures?
235
0.000345
20 017.5
14 000
14 000.0
2.74  10-7
7.20004  108
3
3
6
2
6
3
6
Sig. Figs. in calculations
1.
Addition and Subtraction
Round off the calculated result to match
the number with the leftmost uncertain
(estimated) digit
Sig. Figs. in calculations
Multiplication and Division
Round off the calculated result to the same
number of significant figures as the
measurement with the fewest total significant
figures.
Addition / Subtraction
478.34 + 23.987
1.
2.
3.
Perform normal
mathematical operation
Determine how many
significant figures the
answer should have
Round answer to correct
number of significant
figures
1.
502.327
2.
2
3.
502.33
Multiplication & Division
9.7854 2.1
Perform normal
mathematical
operation
2. Determine how many
sig. figs. the answer
should have.
3. Round the answer to
the correct number of
sig. figs.
1.
1.
4.659714286
2.
2
3.
4.7
Example problems
1.
2.
3.
14.078 - 2.13
0.02 + 0.98734
2.4567 + 135.321
16.020 x 150
2. 0.0422  12
3. 2.65  0.32
1.
11.95
2. 1.01
3. 137.778
1.
2400
2. 0.0035
3. 0.85
1.
Practice Rounding
0.000 345 6 (3)
0.000 346
200.0078 (5)
200.01
589.5 (3)
590.
0.003 007 (2)
0.003 0
2 260 000 (4)
2.260 x 106