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Significant Figures

This guide covers the fundamental rules of significant figures, essential in scientific calculations to ensure precision. Learn how to identify significant figures in various numerical situations, such as digits other than zero, leading zeros, and zeros in decimal numbers. The guide also provides examples and practice questions to strengthen your understanding. Key operations involving addition, subtraction, multiplication, and division are discussed, emphasizing how to round results correctly. Master these concepts for accurate scientific communication.

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Significant Figures

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  1. Significant Figures

  2. Rule 1: Digits other than zero are significant 96 g = 2 Sig Figs 152 g = __________ Sig Figs 61.4 g = 3 Sig Figs 21.567 g = __________ Sig Figs 0.52 g = 2 Sig Figs 0.763 g = __________ Sig Figs

  3. Rule 2: Zeros appearing between nonzero digits are significant 306 g = 3 Sig Figs 40601 g = __________ Sig Figs 5.029 g = 4 Sig Figs 7000.01 g = __________ Sig Figs 4.007 g = 4 Sig Figs 21010101 g = __________ Sig Figs

  4. Rule 3: Zeros appearing in front of all nonzero digits are NOT significant. 0.095897 m = 5 Sig Figs 0.0004526 kg = __________ Sig Figs 0.0009 kg = 1 Sig Fig 0.00721 kg = __________ Sig Figs

  5. Rule 4: Zeros after or to the right of the decimal point are significant. 9.000 000 000 = 10 Sig Figs 7.940 m = __________ Sig Figs 4.7200 m = 5 Sig Figs 1.00000 m = __________ Sig Figs 82.0 m = 3 Sig Figs 789.10 m = __________ Sig Figs

  6. Rule 5: Zeros at the end of a number are significant if a decimal point is present. 7000 kg = 1 Sig Figs 100100 kg = __________ Sig Figs 7000. kg = 4 Sig Figs 200. m = __________ Sig Figs

  7. Rule 6: Only the coefficient in scientific notation is significant, not the power or exponent. 3.64 x 104 m = 3 Sig Figs 0.210 x 103 m = __________ Sig Figs 8.067 x 103 m= 4 Sig Figs 9.416 x 108 m = __________ Sig Figs 6.4800 x 107 m = 5 Sig Figs 410.0 x 103 m = __________ Sig Figs 1 x 104 m = __________ Sig Figs 78400 x 10-3 m = __________ Sig Figs

  8. Addition/Subtraction: After adding or subtracting, round off answer to least accurate number. 13.1 10.5 126.23 + 2.34 9 91.4 15.44 ==> + 76.26 +434.163 95.76 ==> 641.793 ==>

  9. Multiplication/Division: After multiplying or dividing, round off answer to least number of significant figures. 5.63 432.1 632 x 0.20 x 0.002 ÷ 4.3 1.126 ==> ==>

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