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Chapter 2
Measurements
2.4
Significant Figures in
Calculations
1
Basic Chemistry
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Rounding Off Answers
In calculations
• answers must have the
same number of significant
figures as the measured
numbers
• calculated answers are
usually rounded off
• rounding rules are used to
obtain the correct number of
significant figures
2
Basic Chemistry
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Rounding Off Calculated
Answers
• When the first digit dropped is 4 or less, the
retained numbers remain the same.
to round off 45.832 to 3 significant figures
drop the digits 32 = 45.8
• When the first digit dropped is 5 or greater, the
last retained digit is increased by 1.
to round off 2.4884 to 2 significant figures
drop the digits 884 = 2.5 (increase by 0.1)
3
Basic Chemistry
Copyright © 2011 Pearson Education, Inc.
Adding Significant Zeros
• Sometimes a calculated answer requires
more significant digits. Then one or more
zeros are added.
Calculated
Answer
4
1.5
0.2
12
4
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Zeros Added to
Give 3 Significant Figures
4.00
1.50
0.200
12.0
Copyright © 2011 Pearson Education, Inc.
Learning Check
Adjust the following calculated answers to give
answers with three significant figures:
A. 824.75 cm
B. 0.112486 g
C. 8.2 L
5
Basic Chemistry
Copyright © 2011 Pearson Education, Inc.
Solution
Adjust the following calculated answers to give
answers with three significant figures:
A. 825 cm first digit dropped is greater than 5
B. 0.112g
first digit dropped is 4
C. 8.20 L
significant zero added
6
Basic Chemistry
Copyright © 2011 Pearson Education, Inc.
Calculations with Measured
Numbers
In calculations with
measured numbers,
significant figures or
decimal places are
used to determine the
correct number of
figures in the final
answer.
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Basic Chemistry
Copyright © 2011 Pearson Education, Inc.
Multiplication and Division
When multiplying or dividing, use
• the same number of significant figures (SFs) as in
the measurement with the fewest significant
figures
• rounding rules to obtain the correct number of
significant figures
Example
110.5
x
4 SFs
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0.048 = 5.304
2 SFs
calculator
=
5.3 (rounded)
2 SFs
Copyright © 2011 Pearson Education, Inc.
Learning Check
Give an answer for each with the correct
number of significant figures.
A. 2.19 x 4.2
1) 9
B. 4.311 ÷ 0.07
1) 61.59
=
2) 9.2
3) 9.198
=
2) 62
3) 60
C. 2.54 x 0.0028 =
0.0105 x 0.060
1) 11.3
9
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2) 11
3) 0.041
Copyright © 2011 Pearson Education, Inc.
Solution
A. 2.19 x 4.2
B. 4.311 ÷ 0.07
C. 2.54 x 0.0028
0.0105 x 0.060
= 2) 9.2
= 3) 60
= 2) 11
On a calculator, enter each number followed by
the operation key.
2.54 x 0.0028  0.0105  0.060 = 11.28888889
= 11 (rounded off)
10
Basic Chemistry
Copyright © 2011 Pearson Education, Inc.
Addition and Subtraction
When adding or subtracting, use
• the same number of decimal places as the
measurement with the fewest decimal places
• rounding rules to adjust the number of digits in
the answer
25.2
+ 1.34
26.54
26.5
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one decimal place
two decimal places
calculated answer
final answer (one decimal place)
Copyright © 2011 Pearson Education, Inc.
Learning Check
For each calculation, round the answer to give
the correct number of digits.
A. 235.05 + 19.6 + 2 =
1) 257
2) 256.7
B.
12
58.925 - 18.2 =
1) 40.725 2) 40.73
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3) 256.65
3) 40.7
Copyright © 2011 Pearson Education, Inc.
Solution
A. 235.05
+19.6
+ 2
256.65
hundredths place (2 decimal places)
tenths place
(1 decimal place)
ones place
rounds to 257
answer (1)
B.
thousandths place (3 decimal places)
tenths place
(1 decimal place)
round to 40.7
answer (3)
13
58.925
-18.2
40.725
Basic Chemistry
Copyright © 2011 Pearson Education, Inc.