1. 2.3 Significant Figures in Calculations
A calculator is helpful in working problems and doing calculations faster.
Learning Goal Adjust calculated answers to give the correct number of significant figures.

2. Rules for Rounding Off
1. If the first digit to be dropped is 4 or less, then it and all the following digits are dropped from the number. 2. If the first digit to be dropped is 5 or greater, then the last retained digit of the number is increased by 1.
Key Math Skill Rounding Off

3. Study Check
Write the correct value when g is rounded to each of the following:
three significant figures
two significant figures

4. Solution
Write the correct value when g is rounded to each of the following:
To round to three significant figures,
drop the final digits, 57.
increase the last remaining digit by 1.
The answer is 3.15 g.
To round g to two significant figures,
drop the final digits, 457.
do not increase the last number by 1, since the first digit dropped is 4.
The answer is 3.1 g.

5. Multiplication and Division: Measured Numbers
In multiplication or division, the final answer is written so that it has the same number of significant figures (SFs) as the measurement with the fewest significant figures. Example 1 Multiply the following measured numbers: cm × 0.35 cm = (calculator display) = 8.6 cm2 (two significant figures) Multiplying four SFs by two SFs gives us an answer with two SFs.
Core Chemistry Skill Using Significant Figures in Calculations

6. Multiplication and Division: Measured Numbers
Example 2 Multiply and divide the following measured numbers:

7. Adding Significant Zeros
Adding Zeros: When the calculator display contains fewer SFs than needed, add one or more significant zeros to obtain the correct number of significant figures. Example: Multiply and divide the following measured numbers:

8. Study Check
Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures. ×

9. Solution
Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures.

10. Measured Numbers: Addition and Subtraction
In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement with the fewest decimal places.
Example 1 Add the following measured numbers:
Thousandths place
Hundredths place
Tenths place
Calculator display
Answer rounded to the tenths place

11. Measured Numbers: Addition and Subtraction
Example 2 Subtract the following measured numbers:
Hundredths place
− Tenths place
Calculator display
Answer rounded to the tenths place

12. Study Check
Add the following measured numbers: mg mg

13. Solution
Add the following measured numbers: mg Thousandths place Tenths place mg Calculator display mg Answer rounded to the tenths place
Add the following measured numbers: mg mg