 # 1 Chapter 1 Measurements 1.3 Significant Figures in Calculations Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings.

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1 Chapter 1 Measurements 1.3 Significant Figures in Calculations Copyright © 2005 by Pearson Education, Inc. 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 © 2005 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. 45.832 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. 2.4884 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 44.00 1.51.50 0.20.200 12 12.0

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

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. 0.112gFirst digit dropped is 4. C. 8.20 LSignificant 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 © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

8 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: 110.5 x 0.048 = 5.304 = 5.3 (rounded) 4 SF 2 SF calculator 2 SF Multiplication and Division

9 Give an answer for the following 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) 11.32) 11 3) 0.041 Learning Check

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) Solution

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 26.54calculated answer 26.5 answer with one decimal place Addition and Subtraction

12 For each calculation, round the answer to give the correct number of significant figures. 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

13 A. 235.05 +19.6 + 2 256.65 rounds to 257 Answer (1) B. 58.925 -18.2 40.725 round to 40.7Answer (3) Solution