1. Chapter 2 Measurements 2.4 Significant Figures in Calculations
Learning Goal Adjust calculated answers to give the correct number of significant figures.
© 2014 Pearson Education, Inc.

2. calculated answers are usually rounded off
Rounding Off
In calculations
calculated answers are usually rounded off
rounding rules are used to obtain the correct number of significant figures
© 2014 Pearson Education, Inc.

3. Rules for Rounding Off
1. If the first digit to be dropped is 4 or less, then it and all following digits are simply dropped from the number.
2. If the first digit to be dropped is 5 or greater, then the last retained digit is increased by 1.
© 2014 Pearson Education, Inc.

4. Rounding Off and Significant Figures
© 2014 Pearson Education, Inc.

5. Learning Check
Adjust the following calculated answers to give answers with three significant figures:
A cm
B g
8.2 L
© 2014 Pearson Education, Inc.

6. Solution
Adjust the following calculated answers to give answers with three significant figures:
A cm 825 cm
B g g
8.2 L L
© 2014 Pearson Education, Inc.

7. Multiplication and Division with Measured Numbers
In multiplication and division, the final answer is written to have the same number of significant figures (SFs) as the measurement with the fewest SFs.
For example,
24.65 × =  17
4 SF SF Calculator Final answer
© 2014 Pearson Education, Inc.

8. = 4  4.00 Adding Significant Zeros
When the calculator answer is a small whole number and more significant figures are needed, we can add one or more zeros.
For example,
= 
3 SF Calculator Final answer
© 2014 Pearson Education, Inc.

9. Addition and Subtraction with Measured Numbers
In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement having the fewest decimal places.
For example,
Thousandths place
Tenths place
Calculator display
Answer, rounded off to tenths place
© 2014 Pearson Education, Inc.

10. Learning Check
Give an answer for each with the correct number of significant figures.
2.19 × 4.2 =
(1) 9 (2) 9.2 (3) 9.198
B × =
× 0.060
(1) 11.3 (2) (3)
© 2014 Pearson Education, Inc.

11. Solution
Give an answer for each with the correct number of significant figures.
A × = (2) 9.2
B × = (2) 11
× 0.060
© 2014 Pearson Education, Inc.

12. Learning Check
For each calculation, round the answer to give the correct number of digits.
A =
(1) 257 (2) (3)
B – =
(1) (2) (3) 40.7
© 2014 Pearson Education, Inc.

13. Solution A. 235.05 Hundredths place +19.6 Tenths place + 2 Ones place
rounds to answer (1)
B Thousandths place
– Tenths place
rounds to answer (3)
© 2014 Pearson Education, Inc.