Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Chapter 1 Chemistry and Measurements 1.6 Significant Figures in Calculations 1

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Rules for Rounding Off 1. If the first digit to be dropped is 4 or less, then it and all the following digits are 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. 2

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Examples of Rounding 3

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Select the correct value when g is rounded to: A. three significant figures B. two significant figures 4

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Select the correct value when g is rounded to: A. To round to three significant figures, drop the final digits, 57 increase the last remaining digit by 1. The answer is 3.15 g. B. To round g to two significant figures, drop the final digits 457. do not increase the last number by 1 since the first of these digits is 4. The answer is 3.1 g. 5

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Rules for Multiplication and Division In multiplication or division, the final answer is written so it has the same number of significant figures as the measurement with the fewest significant figures (SFs). Example 1: Multiply the following measured numbers: cm x 0.35 cm = (calculator display) = 8.6 cm 2 (2 significant figures) Multiplying 4 SFs by 2 SFs gives us an answer with 2 SFs. 6

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Multiplication and Division with SFs Example 2: Multiply and divide the following measured numbers: 21.5 cm x 0.30 cm = 1.88 cm Put the following into your calculator: 21.5 x 0.30 ÷ 1.88 = = 3.4 cm (2 significant figures) Multiplying 4 SFs by 2 SFs gives us an answer with 2 SFs. 7

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Multiplication and Division with SFs Example 3: Multiply and divide the following measured numbers: 6.0 g = 2.00 g Put the following into your calculator: 6.0 ÷ 2.00 = 3 (calculator display) = 3.0 g (2 significant figures) Add one zero to give 2 significant figures. 8

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures cm x cm = 2.00 cm 9

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures cm x cm = 2.00 cm (3 SF x 4 SF ÷ 3 SF ) = 8.52 cm calculator display and correct significant figures. 10

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Addition and Subtraction In addition or subtraction, the final answer is written so it has the same number of decimal places as the measurement with the fewest decimal places. Example 1: Add the following measured numbers: g three decimal places g two decimal places g one decimal place g (calculator display) = 66.1 g answer rounded to one decimal place 11

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Addition and Subtraction with SFs Example 2: Subtract the following measured numbers: g two decimal places − 3.0 g one decimal place g (calculator display) = 62.1 g answer rounded to one decimal place 12

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Add the following measured numbers: mg mg 13

Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Add the following measured numbers: mg three decimal places mg one decimal place mg (calculator display) = mg answer rounded to one decimal place 14