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Significant Figures

Significant Figures. Purpose . Significant figures are used with any measurement They tell you something about the accuracy of the tool used Sig figs are the known or certain digits in a measurement plus the estimated digit. example.

ruth-riley
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Significant Figures

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  1. Significant Figures

  2. Purpose • Significant figures are used with any measurement • They tell you something about the accuracy of the tool used • Sig figs are the known or certain digits in a measurement plus the estimated digit.

  3. example In the above measurement you are certain it is 64 since the object is between the marked 64 and 65. you then guess the next digit So for this measurement I would say it is 64.3

  4. Rules • All non zero digits are significant because they hold a value. • Zeros may or may not be significant • They are significant when they are: • Between two non zero digits • 1009 • 201 • Are trailing with a decimal • 12.00 • 15.6500

  5. Zeros are not significant when they are: • Leading • 0.000256 • 0.0358 • Trailing without a decimal • 100 • 150 000

  6. Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 100 890 L  5 sig figs 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3 200 000  2 sig figs

  7. Determine the number of significant figures in each measurement using the rules just talked about. Carefully circle the significant figures in each example. State the number of significant figures, and list the rule/s that helped you determine which zeroes are and aren’t significant.

  8. Round each of the following measurements to the indicated number of significant figures. __________ 1) 2.68 to 2 significant figures __________ 2) 47.374 to 3 significant figures __________ 3) 4.165 to 3 significant figures __________ 4) 24 to 1 significant figure __________ 5) 24 to 3 significant figures __________ 6) 0.048 to 2 significant figures __________ 7) 0.06350 to 3 significant figures __________ 8) 0.00045 to 1 significant figure __________ 9) 2007 to 3 significant figures __________ 10) 36.20499 to 4 significant figures __________ 11) 0.023600 to 4 significant figures

  9. 2.7 • 47.4 • 4.17 • 20 • 24.0 • 0.048 • 0.0635 • 0.0005 • 2010 • 36.20 • 0.02360

  10. Rules for Significant Figures in Mathematical Operations • Multiplication and Division:# sig figs in the result equals the number in the least precise measurement used in the calculation. • 6.38 x 2.0 = • 12.76 13 (2 sig figs)

  11. Sig Fig Practice #2 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 23 m2 100.0 g ÷ 23.7 cm3 4.22 g/cm3 4.219409283 g/cm3 0.02 cm x 2.371 cm 0.05 cm2 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 5870 lb·ft 1818.2 lb x 3.23 ft 5872.786 lb·ft 2.9561 g/mL 2.96 g/mL 1.030 g ÷ 2.87 mL

  12. Carry out the following calculations:(Answers should be expressed with the correct number of sig figs!) • 13.62 x 1.7 __________ - because 2. 175.67 x 3.950 __________ - because 3. 2.4 x 15.8 __________ - because 4. 87.35 / 0.016 __________ - because 5. 2.67 / 0.890 __________ - because 6. 46.37 / 20 __________ - because

  13. Rules for Significant Figures in Mathematical Operations • Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. • 6.8 + 11.934 = • 18.734 18.7 (3 sig figs) 6.8 + 11.934 18.734

  14. Sig Fig Practice #3 Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1821.6 lb 1818.2 lb + 3.37 lb 1821.57 lb 0.160 mL 0.16 mL 2.030 mL - 1.870 mL

  15. Carry out the following calculations:(Answers should be expressed with the correct number of sig figs!) 4. 2000 - 46 __________ - because 5. 5.44 – 2.6103 __________ - because 6. 216 - .493 __________ - because 1. 2.0158 + 16.00 __________ - because 2. 35.453 + 1.0079 __________ - because 3. 207.2 + 70.906 __________ - because

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