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Significant Figures Physics

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All nonzero digits are significant 1, 2, 3, 4, 5, 6, 7, 8, 9 Nonzero Digits

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Embedded Zeros are Significant Zeros between other nonzero digits are significant 60.5 3,008 340,506 Embedded Zeros

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Leading Zeros are NOT significant Zeros in front of nonzero digits are not significant 0.75.0032 0.0005 Leading Zeros

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Trailing Zeros in a number with a decimal place ARE significant Zeros that are at the end of a number containing a decimal place ARE significant 5.0 33.20 4800. Trailing Zeros

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Trailing Zeros in a number without a decimal place are NOT significant Zeros that are at the end of a number NOT containing a decimal place are NOT significant 50 3320 4800 Trailing Zeros II

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a) 18.3 b) 183 c).00183 d) 183.0 e) 50 f) 505 g).0050 h) 5000. i) 200.00 j) 0.00220 k) 22020 How many Sig-Figs ?

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a) 18.3 3 b) 183 3 c).00183 3 d) 183.0 4 e) 50 1 f) 505 3 g).0050 2 h) 5000. 4 i) 200.00 5 j) 0.00220 3 k) 22020 4 How many Sig-Figs ?

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The final answer should have the same number of decimal places as the number with the least number of decimal places. 90.3 + 2.23 = 92.53 = 92.5 180.1 + 5.202 + 3.32 = 188.632 = 188.6 Addition & Subtraction

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The final answer has the same number of sig-figs as the number with the least number of sig-figs. 123 x 5.35 = 658.05 = 658 16 x 2 = 32 = 30 16 x 2.0 = 32 = 32 Multiplication & Division

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20.23 + 17.405 +.230 = ________ 20.12 + 5.2 +.245 +100.4 = ________ 5.35 x 20.2 x 5.0 = _______ 2.00 x 500 = _______ 2.5 x 55.5 = ________ Express Result in Sig-Figs

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20.23 + 17.405 +.230 = 37.865=37.86 20.12 + 5.2 +.245 +100.4 = 125.965=126.0 5.35 x 20.2 x 5.0 = 540.35 = 540 2.00 x 500 = 1000 2.5 x 55.5 = 138.75 = 140

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Round Down whenever the digit following the last sig-fig is 0, 1, 2, 3 or 4 Examples of #’s with 3 sig-figs: 50.24 = 50.2 1.0038 = 1.00 230.29 = 230. Round Down

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Round Up whenever the digit following the last sig-fig is a 6, 7, 8 or 9 Examples of #’s with 3 sig-figs: 183.6 = 184.053078 =.0531 23.46 = 23.5 Round Up

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Round UP if the digit following the last sig-fig is a 5 followed by a nonzero digit. Examples with 3 sig-figs: 23.451 = 23.5.018752 =.0188.102531 =.103 Rounding with 5’s I

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Round DOWN if the last sig-fig is an even # and the next digit is a 5, with no other nonzero digits. Round UP if the last sig-fig is an odd # and the next digit is a 5, with no other nonzero digits. Examples of #’s with 3 sig-figs: 12.250 = 12.2 13.25 = 13.2 2.345 = 2.34 7.3850 = 7.38 Rounding with 5’s II

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a) 12.35 b) 100.5 c).0001055 d) 1.2251 e) 230,515 f) 456.5 g) 223.50 h) 1000.5 Express each in 3 Sig-Figs

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a) 12.35 b) 100.5 c).0001055 a) 12.4 b) 100. c).000106 d) 1.2251 e) 230,515 f) 456.5 d) 1.23 e) 231,000 f) 456 g) 223.50 h) 1000.5 g) 224 h) 1000 Answers

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