Transcript Chapter 1
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. Rounding Off In calculations • calculated answers are usually rounded off • rounding rules are used to obtain the correct number of significant figures © 2014 Pearson Education, Inc. Rules for Rounding Off 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. Rounding Off and Significant Figures © 2014 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 © 2014 Pearson Education, Inc. Solution Adjust the following calculated answers to give answers with three significant figures: A. 824.75 cm 825 cm B. 0.112486 g C. 8.2 L © 2014 Pearson Education, Inc. 0.112 g 8.20 L Multiplication and Division with Measured Numbers 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 4 SF © 2014 Pearson Education, Inc. 2 SF = 16.5155 Calculator 17 Final answer Adding Significant Zeros 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. Addition and Subtraction with Measured Numbers 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 + 34.1 36.467 36.5 © 2014 Pearson Education, Inc. Thousandths place Tenths place Calculator display Answer, rounded off to tenths place Learning Check 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. Solution Give an answer for each with the correct number of significant figures. A. 2.19 × 4.2 = B. 2.54 × 0.0028 0.0105 × 0.060 © 2014 Pearson Education, Inc. (2) 9.2 = (2) 11 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. 58.925 – 18.2 = (1) 40.725 (2) 40.73 © 2014 Pearson Education, Inc. (3) 256.65 (3) 40.7 Solution 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 40.7 answer (3) © 2014 Pearson Education, Inc.