Section 5: Significant Figures Cartoon courtesy of Lab-initio.com Unit 1: Matter & Measurement

Suppose you estimate a weight that is between 2.4 lb and 2.5 lb to be 2.46 lb. The first two digits (2 and 4) are known. The last digit (6) is an estimate and involves some uncertainty. All three digits convey useful information, however, and are called significant figures. The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. Significant Figures in Measurements

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

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

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

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

Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures. 1 inch = 2.54 cm, exactly

Sig Fig Practice #1 How many significant figures are in each of the following? m  5 sig figs kg  4 sig figs 100,890 L  5 sig figs 3.29 x 10 3 s  3 sig figs cm  2 sig figs 3,200,000  2 sig figs

Rounding Numbers Example 1: Round to 5 sig figs. Example 2: Round 2056 to 2 sig figs. Look at the digit to the right of the last sig fig. Is it 5 or larger? No. So we get Look at the digit to the right of the last sig fig. Is it 5 or larger? Yes, so round the 0 up to a 1. So we get 2100

Rounding Numbers Example 3: Round to 3 sig figs. Look at the digit to the right of the last sig fig. Is it 5 or larger? No. So we get 91000, except that this does not have 3 sig figs. When this happens, write the number in scientific notation x 10 4

Sig Fig Practice #2 Round to the specified number of significant figures: (3) x 10 6 (2) (2) (3) x (3) x x x 10 -3

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 x 2.0 =  13 (2 sig figs)

Sig Fig Practice # m x 7.0 m CalculationCalculator says:Answer m 2 23 m g ÷ 23.7 cm g/cm g/cm cm x cm cm cm m ÷ 3.0 s m/s240 m/s lb x 3.23 ft lb·ft 5870 lb·ft g ÷ 2.87 mL g/mL g/mL

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 =  18.7 (3 sig figs)

Sig Fig Practice # m m CalculationCalculator says:Answer m 10.2 m g g g 76.3 g 0.02 cm cm cm 2.39 cm L L L709.2 L lb lb lb lb mL mL 0.16 mL mL