1. Significant Figures
Part II: Calculations

2. Objectives When you complete this presentation, you will be able to
determine the number of significant figures in a calculated answer

3. Introduction
We know how to determine the number of significant figures in a measurement.
3.442 g has 4 significant figures
m has 2 significant figures
140 s has 2 significant figures
mL has 3 significant figures
Now, we need to learn how to use those measurements in calculations.

4. Rounding
In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.
The calculated value must be rounded to make it consistent with the measurements.

5. Rounding
To round, we need to determine how many significant figures the answer needs to have.
This depends on the measurements and the math process used to determine the answer.
We will cover the details of that later in the presentation.
First, let’s practice rounding numbers to a proper number of significant figures.

6. Rounding How do we round a numerical value?
We use the same rules we have always used.
If the digit to the immediately to the right of the last significant digit is less than 5, we drop the rest of the digits and the value of the last significant digit remains the same.
Round to 3 sig figs ➠ ➠ 45.2
Round to 2 sig figs ➠ ➠ 0.85

7. Rounding How do we round a numerical value?
We use the same rules we have always used.
If the digit to the immediately to the right of the last significant digit is 5 or greater we drop the rest of the digits and the value of the last significant digit is increased by 1.
Round to 3 sig figs ➠ ➠ 62.6
Round to 2 sig figs ➠ ➠ 0.055

8. Rounding
Example 1: Round each of the following numbers to the indicated number of significant figures:
54, m to 3 sig figs
kg to 4 sig figs
s to 1 sig fig
cm to 2 sig figs
355,000 km to 2 sig figs
L to 3 sig figs
54,500 m kg
40 s
0.78 cm
360,000 km L

9. Calculations – addition and subtraction
The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.
For example:
12.52 m m
The m measurement has the least number of decimal places. m m

10. Calculations – addition and subtraction
The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.
For example:
12.52 m m
That measurement will control the number of decimal places in the answer. m m

11. Calculations – addition and subtraction
The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.
For example:
12.52 m m
The reported answer should be
369.8 m m m

12. Calculations – addition and subtraction
Example 2: Perform each operation. Express the answer in the correct number of sig figs.
61.2 m m m
14.2 g g g
35 s s s
9.44 kg – 2.11 kg
1.36 cm cm
34.61 mL – 17.3 mL
79.2 m
23.8 g
109 s
7.33 kg
11.53 cm
17.3 mL

13. Calculations – multiplication and division
The answer to a multiplication or division calculation should be rounded to the same number of significant digits as the measurement with the least number of significant digits.
For example:
7.55 m
× m
The 0.34 m measurement has the least number of significant digits (2).
2.567 m2

14. Calculations – multiplication and division
The answer to a multiplication or division calculation should be rounded to the same number of significant digits as the measurement with the least number of significant digits.
For example:
7.55 m
× m
That measurement will control the number of decimal places in the answer.
2.567 m2

15. Calculations – multiplication and division
The answer to a multiplication or division calculation should be rounded to the same number of significant digits as the measurement with the least number of significant digits.
For example:
7.55 m
× m
The reported answer should be
2.6 m2
2.567 m2

16. Calculations – multiplication and division
Example 3: Perform each operation. Express the answer in the correct number of sig figs.
2.10 m × 0.70 m
kg ÷ 8.4
8.3 m × 2.22 m
8432 kg ÷ 12.5
32 s ×
34.61 mL ÷ 17.3
1.5 m2
0.29 kg
18 m2
675 kg
480 s
2.00 mL

17. Summary
A calculated answer cannot be more precise than the least precise measurement from which it was calculated.
The calculated value must be rounded to make it consistent with the measurements.

18. Summary Rules for rounding:
If the digit to the immediately to the right of the last significant digit is less than 5, we drop the rest of the digits and the value of the last significant digit remains the same.
If the digit to the immediately to the right of the last significant digit is 5 or greater we drop the rest of the digits and the value of the last significant digit is increased by 1.

19. Summary Significant figures in calculations:
The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not digits) as the measurement with the least number of decimal places.
The answer to a multiplication or division calculation should be rounded to the same number of significant digits as the measurement with the least number of significant digits.