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Chapter 1 Chemistry and Measurements

Chapter 1 Chemistry and Measurements. 1.6 Significant Figures in Calculations. 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.

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Chapter 1 Chemistry and Measurements

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  1. Chapter 1 Chemistry and Measurements 1.6 Significant Figures in Calculations

  2. 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.

  3. Examples of Rounding

  4. Learning Check Select the correct value when 3.1457 g is rounded to: A. three significant figures B. two significant figures

  5. Solution Select the correct value when 3.1457 g is rounded to: A. 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. B. 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 of these digits is 4. The answer is 3.1 g.

  6. 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: 24.66 cm x 0.35 cm = 8.631 (calculator display) = 8.6 cm2 (2 significant figures) Multiplying 4 SFs by 2 SFs gives us an answer with 2 SFs.

  7. 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 = 3.430851063 = 3.4 cm(2 significant figures) Multiplying 4 SFs by 2 SFs gives us an answer with 2 SFs.

  8. 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.

  9. Learning Check Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures. 5.00 cm x 3.408 cm = 2.00 cm

  10. Solution Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures. 5.00 cm x 3.408 cm = 2.00 cm (3 SF x 4 SF ÷ 3 SF ) = 8.52 cm calculator display and correct significant figures.

  11. 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: 2.012 g three decimal places 61.09 g two decimal places + 3.0 g one decimal place 66.102 g (calculator display) = 66.1 g answer rounded to one decimal place

  12. Addition and Subtraction with SFs Example 2: Subtract the following measured numbers: 65.09 g two decimal places − 3.0 g one decimal place 62.09 g (calculator display) = 62.1 g answer rounded to one decimal place

  13. Learning Check Add the following measured numbers: 82.409 mg + 22.0 mg

  14. Solution Add the following measured numbers: 82.409 mg three decimal places + 22.0 mg one decimal place 104.409 mg (calculator display) = 104.4 mg answer rounded to one decimal place

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