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**Significant Figures in Calculations**

Chapter 1 Measurements Significant Figures in Calculations Timberlake lecture plus

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**Significant Figures in Measurement**

The numbers reported in a measurement are limited by the measuring tool Significant figures in a measurement include the known digits plus one estimated digit Timberlake lecture plus

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**Counting Significant Figures**

Number of Significant Figures 38.15 cm 4 5.6 ft 2 65.6 lb ___ m ___ Complete: All non-zero digits in a measured number are (significant or not significant). Timberlake lecture plus

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**Timberlake lecture plus**

Leading Zeros Number of Significant Figures 0.008 mm 1 oz 3 lb ____ mL ____ Complete: Leading zeros in decimal numbers are (significant or not significant). Timberlake lecture plus

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**Timberlake lecture plus**

Sandwiched Zeros Number of Significant Figures 50.8 mm 3 2001 min 4 0.702 lb ____ m ____ Complete: Zeros between nonzero numbers are (significant or not significant). Timberlake lecture plus

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**Timberlake lecture plus**

Trailing Zeros Number of Significant Figures 25,000 in 200 yr 1 48,600 gal 3 25,005,000 g ____ Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders. Timberlake lecture plus

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**Timberlake lecture plus**

Learning Check A. Which answers contain 3 significant figures? 1) ) ) 4760 B. All the zeros are significant in 1) ) ) x 103 C. 534,675 rounded to 3 significant figures is 1) ) 535, ) 5.35 x 105 Timberlake lecture plus

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**Timberlake lecture plus**

Solution A. Which answers contain 3 significant figures? 2) ) 4760 B. All the zeros are significant in 2) ) x 103 C. 534,675 rounded to 3 significant figures is 2) 535, ) 5.35 x 105 Timberlake lecture plus

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**Timberlake lecture plus**

Learning Check In which set(s) do both numbers contain the same number of significant figures? 1) and 22.00 2) and 40 3) and 150,000 Timberlake lecture plus

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**Timberlake lecture plus**

Solution In which set(s) do both numbers contain the same number of significant figures? 3) and 150,000 Timberlake lecture plus

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**Timberlake lecture plus**

Learning Check SF3 State the number of significant figures in each of the following: A m B L C g D m E. 2,080,000 bees Timberlake lecture plus

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**Timberlake lecture plus**

Solution A m 2 B L 4 C g 1 D m 3 E. 2,080,000 bees 3 Timberlake lecture plus

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**Significant Numbers in Calculations**

A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing Timberlake lecture plus

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**Adding and Subtracting**

The answer has the same number of decimal places as the measurement with the fewest decimal places. one decimal place two decimal places 26.54 answer one decimal place Timberlake lecture plus

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**Timberlake lecture plus**

Learning Check In each calculation, round the answer to the correct number of significant figures. A = 1) ) ) 257 B = 1) ) ) 40.7 Timberlake lecture plus

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**Timberlake lecture plus**

Solution A = 2) 256.8 B = 3) 40.7 Timberlake lecture plus

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**Multiplying and Dividing**

Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures. Timberlake lecture plus

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**Timberlake lecture plus**

Learning Check A X 4.2 = 1) ) ) B ÷ = 1) ) ) 60 C X = X 0.060 1) ) ) Timberlake lecture plus

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**Timberlake lecture plus**

Solution A X = 2) 9.2 B ÷ = 3) 60 C X = 2) X 0.060 Continuous calculator operation = x Timberlake lecture plus

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