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Precision and Accuracy Uncertainty in Measurements Precision and Accuracy Uncertainty a measurement can only be as good as the instrument or the method used to make it. Ex. Cop’s Radar Gun vs. Car’s Speedometer. Bank sign Thermometer vs. your skin. Precision and Accuracy Accepted Value A measurement deemed by scientists to be the “true measurement.” Accuracy The Closeness or proximity of a measurement to the accepted value. Precision and Accuracy Precision A proven agreement between the numerical values of a set of measurements done by the same instrument and/or method. . Precision and Accuracy Significant Figures are the digits used to represent the precision of a measurement. SIG. FIGS. are equal to all known measurements plus one estimated digit. Rules for Significant Digits 1) ALL NON-ZERO DIGITS ARE SIGNIFICANT 2) EXACT NUMBERS have an infinite number of significant numbers. Exact #s are #s that are defined not measured. Numbers found by counting or used for conversions such as 100 cm = 1 m. 3) Zeros can be both significant or insignficant Rules for Significant Digits The Three Classes of Zeros A. Leading Zeros Zeros that precede all of the non-zero digits are NOT significant. Ex. 0.0025 mg has only 2 sig. figs.( the 2 & 5) all three zeros are not significant. Rules for Significant Digits B. Captive Zeros Zeros between two or more nonzero or significant digits ARE significant. Ex. 10.08 grams All four #s are significant Rules for Significant Digits C) Trailing Zeros Zeros located to the right of a nonzero or significant digit ARE Significant ONLY if there is a decimal in the measurement. Ex. 20.00 lbs Has four sig. figs. 2000 lbs Has only 1 sig. figs Calculations with Significant Digits Multiplication or Division The product or quotient must be Rounded so that it contains the same # of digits as the least significant measurement in the problem. Ex. ( 2.2880 ml )(0.305 g/ml ) = 0.69784 g Ans. Must be rounded to 3 sig. figs. mass = 0.698 g Calculations with Significant Digits Addition and Subtraction The sum of two or more measurements must be rounded to the same number of digits to the right of the decimal point as the least precise measurement in the problem. 2.00003 g EX. 10.234 g only one digit + 333.3 g = 345.53403 g 345.5 g