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Chapter 2 Lecture Basic Chemistry Fourth Edition Chapter 2 Measurements 2.4 Significant Figures in Calculations Learning Goal Adjust calculated answers to give the correct number of significant figures. © 2014 Pearson Education, Inc.

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In calculations calculated answers are usually rounded off rounding rules are used to obtain the correct number of significant figures © 2014 Pearson Education, Inc. Rounding Off

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1.If the first digit to be dropped is 4 or less, then it and all following digits are simply dropped from the number. 2.If the first digit to be dropped is 5 or greater, then the last retained digit is increased by 1. © 2014 Pearson Education, Inc. Rules for Rounding Off

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© 2014 Pearson Education, Inc. Rounding Off and Significant Figures

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Adjust the following calculated answers to give answers with three significant figures: A.824.75 cm B.0.112486 g C.8.2 L © 2014 Pearson Education, Inc. Learning Check

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Adjust the following calculated answers to give answers with three significant figures: A.824.75 cm825 cm B.0.112486 g0.112 g C.8.2 L8.20 L © 2014 Pearson Education, Inc. Solution

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In multiplication and division, the final answer is written to have the same number of significant figures (SFs) as the measurement with the fewest SFs. For example, 24.65 × 0.67 = 16.5155 17 4 SF 2 SF Calculator Final answer © 2014 Pearson Education, Inc. Multiplication and Division with Measured Numbers

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When the calculator answer is a small whole number and more significant figures are needed, we can add one or more zeros. For example, = 4 4.00 3 SF Calculator Final answer © 2014 Pearson Education, Inc. Adding Significant Zeros

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In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement having the fewest decimal places. For example, 2.367 Thousandths place + 34.1 Tenths place 36.467 Calculator display 36.5 Answer, rounded off to tenths place © 2014 Pearson Education, Inc. Addition and Subtraction with Measured Numbers

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Give an answer for each with the correct number of significant figures. A.2.19 × 4.2 = (1) 9(2) 9.2(3) 9.198 B.2.54 × 0.0028 = 0.0105 × 0.060 (1) 11.3(2) 11 (3) 0.041 © 2014 Pearson Education, Inc. Learning Check

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Give an answer for each with the correct number of significant figures. A. 2.19 × 4.2 =(2) 9.2 B. 2.54 × 0.0028 = (2) 11 0.0105 × 0.060 © 2014 Pearson Education, Inc. Solution

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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 © 2014 Pearson Education, Inc. Learning Check

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A. 235.05 Hundredths place +19.6 Tenths place + 2 Ones place 256.65 rounds to 257 answer (1) B. 58.925 Thousandths place –18.2 Tenths place 40.725 rounds to 40.7answer (3) © 2014 Pearson Education, Inc. Solution

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