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General, Organic, and Biological Chemistry Fourth Edition Karen Timberlake 1.6 Significant Figures in Calculations Chapter 1 Chemistry and Measurements © 2013 Pearson Education, Inc. Lectures

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 2 Calculations with Measured Numbers The number of significant figures in measured numbers are used to limit the number of significant figures in the final answer. Calculators do not provide the appropriate number of significant figures.

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 3 Rounding Off To represent the appropriate number of significant figures, we use "rules for rounding." 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 of the number is increased by 1.

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 4 Rounding Off

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 5 When multiplying or dividing use the same number of significant figures (SF) as the measurement with the fewest significant figures, and the rounding rules to obtain the correct number of significant figures. Multiplication and Division

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 6 Give an answer for the following with the correct number of significant figures. A. 9 B. 9.2 C. 9.198 A. 61.59 B. 62 C. 60 3. A. 11.3B. 11 C. 0.041 Learning Check

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 7 Give an answer for the following with the correct number of significant figures. On a calculator, enter each number followed by the operation key. Solution

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 8 Sometimes we add one or more significant zeros to the calculator display in order to obtain the correct number of significant figures needed. Example: Suppose the calculator display is 4, and you need 3 significant figures. 4 becomes 4.00 1 SF 3 SF Adding Significant Zeros

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 9 When adding or subtracting, use the same number of decimal places as the measurement with the fewest decimal places and the rounding rules to adjust the number of digits in the answer. one decimal place two decimal places calculated answer final answer (with one decimal place) Addition and Subtraction

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 10 For each calculation, round the answer to give the correct number of decimal places. A. 257 B. 256.7C. 256.65 A. 40.725 B. 40.73C. 40.7 Learning Check

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© 2013 Pearson Education, Inc. Chapter 1, Section 6 11 For each calculation, round the answer to give the correct number of decimal places. Solution

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