The document discusses significant figures and rounding in calculations involving measurement data. It explains that calculated answers should have the same number of significant figures as the measured values used. For multiplication and division, the final answer should have the same number of significant figures as the value with the fewest significant figures. For addition and subtraction, the final answer should have the same number of decimal places as the value with the fewest decimal places. Examples are provided to demonstrate rounding calculated answers to the correct number of significant figures or decimal places.

1. Chapter 2 Measurements 2.4 Significant Figures in Calculations Basic Chemistry Copyright © 2011 Pearson Education, Inc.

2. 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 Basic Chemistry Copyright © 2011 Pearson Education, Inc.

3. 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) Basic Chemistry Copyright © 2011 Pearson Education, Inc.

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 4 4.00 1.5 1.50 0.2 0.200 12 12.0 Basic Chemistry Copyright © 2011 Pearson Education, Inc.

5. 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 Basic Chemistry Copyright © 2011 Pearson Education, Inc.

6. 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 Basic Chemistry Copyright © 2011 Pearson Education, Inc.

7. 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. Basic Chemistry Copyright © 2011 Pearson Education, Inc.

8. 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 0.048 = 5.304 = 5.3 (rounded) 4 SFs 2 SFs calculator 2 SFs Multiplication and Division Basic Chemistry Copyright © 2011 Pearson Education, Inc.

9. Give an answer for each with the correct number of significant figures. A. 2.19 x 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.59 2) 62 3) 60 C. 2.54 x 0.0028 = 0.0105 x 0.060 1) 11.3 2) 11 3) 0.041 Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.

10. A. 2.19 x 4.2 = 2) 9.2 B. 4.311 ÷ 0.07 = 3) 60 C. 2.54 x 0.0028 = 2) 11 0.0105 x 0.060 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 ) Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.

11. 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 one decimal place + 1.34 two decimal places 26.54 calculated answer 26.5 final answer (one decimal place) Addition and Subtraction Basic Chemistry Copyright © 2011 Pearson Education, Inc.

12. For each calculation, round the answer to give the correct number of digits. A. 235.05 + 19.6 + 2 = 1) 257 2) 256.7 3) 256.65 B. 58.925 - 18.2 = 1) 40.725 2) 40.73 3) 40.7 Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.

13. A. 235.05 hundredths place (2 decimal places) +19.6 tenths place (1 decimal place) + 2 ones place 256.65 rounds to 257 answer (1) B. 58.925 thousandths place (3 decimal places) -18.2 tenths place (1 decimal place) 40.725 round to 40.7 answer (3) Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.