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Rule for Using Sig Figs in Math:

This guide explains how to use significant figures (sig figs) in mathematical calculations, emphasizing that the precision of your result cannot exceed that of your least precise number. It covers rules for multiplication, division, addition, and subtraction with detailed examples. Learn how to round appropriately according to the number of significant figures in your measurements. Whether you're multiplying volumes or adding lengths, this resource will help ensure your calculations reflect the appropriate level of precision.

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Rule for Using Sig Figs in Math:

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  1. Rule for Using Sig Figs in Math: The result of your calculations can never be more precise than your LEAST precise number!

  2. Example • You may know very precisely that the volume of your bucket is 401234.2 ml , but if you have a very uncertain number of drops/ml (24 drops/ml)… 24 drops/ml x 401234.2 ml = 9629620.8 drops? -or- 9600000 drops?

  3. Multiplication/Division • Round to the same number of places as the number with the least sig figs. • 12 x 230.1 = 2761.2 (calculator) = 2800 • 0.00325 / .120 = 0.0270833333333 (calc) = 0.0271 = 70.65 (calc) = 70

  4. Addition and Subtraction • Round to the last sig fig in the most uncertain number. 9.12 + 4.3 + 6.01 = ? 19.43 (calc) 9.12 4.3 + 6.01 19.4

  5. 0.11001 - 2.12 - 12 = ? -14.00999 (calc) 0.11001 2.12 -12______ -14

  6. Try these on your own…

  7. 3.414 s + 10.02 s + 58.325 s + 0.00098 s

  8. = 71.76 s

  9. 1884 kg + 0.94 kg + 1.0 kg + 9.778 kg = 1896 kg

  10. 2104.1 m – 463.09 m = 1641.0 m

  11. 2.326 hrs – 0.10408 hrs = 2.222 hrs

  12. 10.19 m x 0.013 m = 0.13 m2

  13. 140.01 cm x 26.042 cm x 0.0159 cm = 58.0 cm

  14. 80.23 m ÷ 2.4 s = 33 m/s

  15. 4.301 kg ÷ 1.9 cm3 = 2.3 kg/cm3

  16. What if Multiplication/Division and Addition/Subtraction are combined? Do it in steps, according to the order of operations…

  17. (2.39 m – 0.2 m)12.43 s = 2.2 m 12.43 s = 0.18 m/s

  18. 2.00 m – 0.500(0 + 3.0 m/s)(3 s) = 2.00 m – 0.500(3.0 m/s)(3s) = 2.00 m – 5 m = -3 m

  19. 0.37 m – 1.22 m – (4 m/s)(3.0020 s)0.5000 x (1.0021s)2 = 0.37m – 1.22m – 10m 0.5000 x (1.0021s)2 = _____- 10 m______ 0.5000 x (1.0021s)2 = - 20 m/s2

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