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Chapter 2 Measurements 2.4 Significant Figures in Calculations 1 Basic Chemistry Copyright © 2011 Pearson Education, Inc. 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 2 Basic Chemistry Copyright © 2011 Pearson Education, Inc. 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) 3 Basic Chemistry Copyright © 2011 Pearson Education, Inc. Adding Significant Zeros • Sometimes a calculated answer requires more significant digits. Then one or more zeros are added. Calculated Answer 4 1.5 0.2 12 4 Basic Chemistry Zeros Added to Give 3 Significant Figures 4.00 1.50 0.200 12.0 Copyright © 2011 Pearson Education, Inc. 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 5 Basic Chemistry Copyright © 2011 Pearson Education, Inc. 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 6 Basic Chemistry Copyright © 2011 Pearson Education, Inc. 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. 7 Basic Chemistry Copyright © 2011 Pearson Education, Inc. Multiplication and Division 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 4 SFs 8 Basic Chemistry 0.048 = 5.304 2 SFs calculator = 5.3 (rounded) 2 SFs Copyright © 2011 Pearson Education, Inc. Learning Check Give an answer for each with the correct number of significant figures. A. 2.19 x 4.2 1) 9 B. 4.311 ÷ 0.07 1) 61.59 = 2) 9.2 3) 9.198 = 2) 62 3) 60 C. 2.54 x 0.0028 = 0.0105 x 0.060 1) 11.3 9 Basic Chemistry 2) 11 3) 0.041 Copyright © 2011 Pearson Education, Inc. Solution A. 2.19 x 4.2 B. 4.311 ÷ 0.07 C. 2.54 x 0.0028 0.0105 x 0.060 = 2) 9.2 = 3) 60 = 2) 11 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) 10 Basic Chemistry Copyright © 2011 Pearson Education, Inc. Addition and Subtraction 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 + 1.34 26.54 26.5 11 Basic Chemistry one decimal place two decimal places calculated answer final answer (one decimal place) Copyright © 2011 Pearson Education, Inc. Learning Check For each calculation, round the answer to give the correct number of digits. A. 235.05 + 19.6 + 2 = 1) 257 2) 256.7 B. 12 58.925 - 18.2 = 1) 40.725 2) 40.73 Basic Chemistry 3) 256.65 3) 40.7 Copyright © 2011 Pearson Education, Inc. Solution A. 235.05 +19.6 + 2 256.65 hundredths place (2 decimal places) tenths place (1 decimal place) ones place rounds to 257 answer (1) B. thousandths place (3 decimal places) tenths place (1 decimal place) round to 40.7 answer (3) 13 58.925 -18.2 40.725 Basic Chemistry Copyright © 2011 Pearson Education, Inc.