 # Significant Figures. Purpose Significant figures are used with any measurement Significant figures are used with any measurement They tell you something.

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Significant Figures

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

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

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

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

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 10 3 s  3 sig figs 0.0054 cm  2 sig figs 3 200 000  2 sig figs

28.6___ sig figs 3 440.00___ sig figs 910___ sig figs 4.06 x 10 3 ___ sig figs 0.006 700___ sig figs 804.05___ sig figs 0.014 403___ sig figs 1.44 x 10 -2 ___ sig figs 400___ sig figs 30 000.___ sig figs 1002___ sig figs 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.

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) 24to 1 significant figure __________ 5) 24to 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) 0.023600to 4 significant figures

1. 2.7 2. 47.4 3. 4.17 4. 20 5. 24.0 6. 0.048 7. 0.0635 8. 0.0005 9. 2010 10. 36.20 11. 0.02360

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. 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 = 6.38 x 2.0 = 12.76  13 (2 sig figs) 12.76  13 (2 sig figs)

Sig Fig Practice #2 3.24 m x 7.0 m CalculationCalculator says:Answer 22.68 m 2 23 m 2 100.0 g ÷ 23.7 cm 3 4.219409283 g/cm 3 4.22 g/cm 3 0.02 cm x 2.371 cm 0.04742 cm 2 0.05 cm 2 710 m ÷ 3.0 s 236.6666667 m/s240 m/s 1818.2 lb x 3.23 ft5872.786 lb·ft 5870 lb·ft 1.030 g ÷ 2.87 mL 2.9561 g/mL2.96 g/mL

Carry out the following calculations: (Answers should be expressed with the correct number of sig figs!) 1. 1. 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

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. 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 = 6.8 + 11.934 = 18.734  18.7 (3 sig figs) 18.734  18.7 (3 sig figs) 6.8 + 11.934 18.734

Sig Fig Practice #3 3.24 m + 7.0 m CalculationCalculator says:Answer 10.24 m 10.2 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L709.2 L 1818.2 lb + 3.37 lb1821.57 lb 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL

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

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