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Significant Figures, Precision, and Accuracy

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Significant Figures Significant figures are numbers that mean something when reporting a value. Just because your calculator gives out the value 0.5384615 when 7.00 is divided by 13.0, to a scientist not all of the numbers in 0.5384615 have meaning. Significant figures reflect the significance of the measurements upon which the scientific calculation is based.

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Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures. 3456 has 4 sig figs.

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Rules for Counting Significant Figures - Details Zeros Leading zeros do not count as significant figures. 0.0486 has 3 sig figs.

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Rules for Counting Significant Figures - Details Zeros Captive zeros always count as significant figures. 16.07 has 4 sig figs.

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Rules for Counting Significant Figures - Details Zeros Trailing zeros are significant only if the number contains a decimal point. 9.300 has 4 sig figs.

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Rules for Counting Significant Figures - Details Exact numbers (such as those in conversion factors) have an infinite number of significant figures. 1 inch = 2.54 cm, exactly

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Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m 17.10 kg 100,890 L 3.29 x 10 3 s 0.0054 cm 3,200,000

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Use the Rounding Poem to Round Numbers Correctly Find your number Look right next door 4 or less, just ignore 5 or greater add one more! Round 4.167 to the closest hundredths 4.167Find your number Look right next door 4.17

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

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

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Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. If the true value were 5.00 and three measured values 2.0, 6.0, and 7.0 average out to 5.0 (as they do), then that set of measurements would be accurate. Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate

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