1. Significant Figures in
Chapter Measurements
1.3
Significant Figures in
Calculations
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Publishing as Benjamin Cummings

2. Rounding Off Calculated Answers
In calculations,
answers must have the same number of significant figures as the measured numbers.
often, a calculator answer must be rounded off.
rounding rules are used to obtain the correct number of significant figures.
Copyright © by Pearson Education, Inc.
Publishing as Benjamin Cummings

3. Rounding Off Calculated Answers
When the first digit dropped is 4 or less,
the retained numbers remain the same.
rounded to 3 significant figures
drops the digits 32 = 45.8
When the first digit dropped is 5 or greater,
the last retained digit is increased by 1.
rounded to 2 significant figures
drops the digits 884 = 2.5 (increase by 0.1)

4. Adding Significant Zeros
Sometimes a calculated answer requires more significant digits. Then, one or more zeros are added.
Calculated Zeros Added to
Answer Give 3 Significant Figures

5. Learning Check Adjust the following calculated answers to give
answers with three significant figures.
A cm
B g
C L

6. Solution Adjust the following calculated answers to give answers
with three significant figures
A cm First digit dropped is greater than 5.
B g First digit dropped is 4.
C L Significant zero is added.

7. Calculations with Measured Numbers
In calculations with
measured numbers,
significant figures or
decimal places are
counted to determine
the number of figures in
the final answer.
Copyright © by Pearson Education, Inc.
Publishing as Benjamin Cummings

8. Multiplication and Division
When multiplying or dividing use
the same number of significant figures as the measurement with the fewest significant figures.
rounding rules to obtain the correct number of significant figures.
Example:
x = = (rounded)
4 SF SF calculator SF

9. Learning Check Give an answer for the following with the correct
number of significant figures.
A x =
1) ) )
B ÷ =
1) ) ) 60
C x =
x 0.060
1) ) )

10. Solution
A x = 2) 9.2
B ÷ = 3) 60
C x = 2) 11 x
On a calculator, enter each number followed by the operation key.
2.54 x   =
= 11 (rounded)

11. 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.
one decimal place
two decimal places
26.54 calculated answer
answer with one decimal place

12. Learning Check For each calculation, round the answer to give the
correct number of significant figures.
A =
1) ) )
B =
1) ) ) 40.7

13. Solution A. 235.05 +19.6 + 2 256.65 rounds to 257 Answer (1) B. 58.925
+ 2
rounds to Answer (1) B
-18.2
round to Answer (3)