2.3 Significant Figures in Calculations A calculator is helpful in working problems and doing calculations faster. Learning Goal Adjust calculated answers to give the correct number of significant figures.

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. Key Math Skill Rounding Off

Study Check Write the correct value when 3.1457 g is rounded to each of the following: three significant figures two significant figures

Solution Write the correct value when 3.1457 g is rounded to each of the following: To round 3.1457 to three significant figures, drop the final digits, 57. increase the last remaining digit by 1. The answer is 3.15 g. To round 3.1457 g to two significant figures, drop the final digits, 457. do not increase the last number by 1, since the first digit dropped is 4. The answer is 3.1 g.

Multiplication and Division: Measured Numbers In multiplication or division, the final answer is written so that it has the same number of significant figures (SFs) as the measurement with the fewest significant figures. Example 1 Multiply the following measured numbers: 24.66 cm × 0.35 cm = 8.631 (calculator display) = 8.6 cm2 (two significant figures) Multiplying four SFs by two SFs gives us an answer with two SFs. Core Chemistry Skill Using Significant Figures in Calculations

Multiplication and Division: Measured Numbers Example 2 Multiply and divide the following measured numbers:

Adding Significant Zeros Adding Zeros: When the calculator display contains fewer SFs than needed, add one or more significant zeros to obtain the correct number of significant figures. Example: Multiply and divide the following measured numbers:

Study Check Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures. ×

Solution Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures.

Measured Numbers: Addition and Subtraction In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement with the fewest decimal places. Example 1 Add the following measured numbers: 2.012 Thousandths place 61.09 Hundredths place + 3.0 Tenths place 66.102 Calculator display 66.1 Answer rounded to the tenths place

Measured Numbers: Addition and Subtraction Example 2 Subtract the following measured numbers: 65.09 Hundredths place − 3.0 Tenths place 62.09 Calculator display 62.1 Answer rounded to the tenths place

Study Check Add the following measured numbers: 82.409 mg + 22.0 mg

Solution Add the following measured numbers: 82.409 mg Thousandths place Tenths place 104.409 mg Calculator display 104.4 mg Answer rounded to the tenths place Add the following measured numbers: 82.409 mg + 22.0 mg