ࡱ> gif'` bjbjLULU '.?.? ^^^^t$ b0h"&&&N///////$1h24^0W@0^^&N 0!!!^R&(N/!/!!-h"/N ߊ|W./200b0g.4/ 4 //4/L!00 b0 $ F$j|^^^^^^ Name: _______________________________ Period: ____ Date: ______________________ Significant Figures It is important to be honest when reporting a measurement, so that it does not appear to be more accurate than the equipment used to make the measurement allows. We can achieve this by controlling the number of digits, or significant figures, used to report the measurement. Every measurement has a degree of uncertainty associated with it. The uncertainty derives from the measuring device and from the skill of the person doing the measuring. Let's use length measurement example. Say you are in a chemistry lab, measure the length of a metal wire using one ruler shown at the bottom with 1 cm increment. You measure it to be 2.5 cm. You are sure that your wire is between 2cm and 3cm, probably close to 2.5cm. Then your lab partner finds another ruler with 0.1 cm increment marks (ruler on top). Now you can measure between 2.5 and 2.6 cm pretty reliably. It would b however, untrue to report that you measured to 2.550cm using this ruler because you did not measure your length to the nearest thousandths. You would report your measurement using significant figures. These include all of the digits you know for certain plus the last digit, which contains some uncertainty. Rules for Counting Significant Figures 1. Nonzero integers always count as significant figures. Example: 3456 has 4 sig figs. 2. Zeros - Leading zeros do not count as significant figures. Example: 0.0486 has 3 sig figs. 3. Zeros - Captive zeros always count as significant figures. Example: 16.07 has 4 sig figs. Zeros - Trailing zeros are significant only if the number contains a decimal point. Example: 9.300 has 4 sig figs. 5. Exact numbers have an infinite number of significant figures. Example: 1 inch = 2.54 cm, exactly Rules for Significant Figures in Mathematical Operations 1. Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. Example: 6.38 x 2.0 = 12.76 = 13 (2 sig figs) 2. Addition and Subtraction: # sig figs in the result equals the number of decimal places in the least precise measurement. 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