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1 Chapter 2 Measurements 2.4 Significant Figures in Calculations Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

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2 Rounding Off Answers Often, the correct answer Requires that a calculated answer be rounded off. Uses rounding rules to obtain the correct answer with the proper number of significant figures. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

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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)

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4 Adding Significant Zeros Occasionally, a calculated answer requires more significant digits. Then one or more zeros are added. CalculatedZeros added to answergive 3 significant figures 44.00 1.51.50 0.20.200 12 12.0

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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

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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.

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7 Calculations with Measured Numbers In calculations with measured numbers, Significant figures are counted or Place values are determined to give The correct number of figures in the final answer. Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings

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8 When multiplying or dividing The answer has the same number of significant figures as in the measurement with the fewest significant figures. Rounding rules are used 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

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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) 11.32) 11 3) 0.041 Learning Check

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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

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11 When adding or subtracting use The same number of digits as the measurement whose last digit has the highest place value. Use 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

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12 For each calculation, round the answer to give the correct number of digits. A. 235.05 + 19.6 + 2 = 1) 257 2) 256.73) 256.65 B. 58.925 - 18.2= 1) 40.725 2) 40.733) 40.7 Learning Check

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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 40.7Answer (3) Solution

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