# Significant Figures in Calculations

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Significant Figures in Calculations
Chapter 1 Measurements Significant Figures in Calculations Timberlake lecture plus

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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