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Precision and Accuracy Uncertainty in Measurements

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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.

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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. The difference between the actual measurement and the accepted value is called the ABSOLUTE ERROR.

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Precision and Accuracy Precision A proven agreement between the numerical values of a set of measurements done by the same instrument and/or method. The Difference between the set of measurements is expressed as Absolute Deviation..

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Precision and Accuracy Precision refers to the reproducibility of a measurement. 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.

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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

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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.

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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

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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

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Calculations with Significant Digits Addition and Subtraction:: The answer must be Rounded so that it contains the same # of digits to the right of the decimal point as there are in the measurement with the smallest # of digits to the right of the decimal. 13.89 years + 0.00045 years = 13.89045 years Rounds to 13.89 years 2 places to the Rt.

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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

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Rules for Rounding Numbers If the digit immediately to the right of the last significant figure you want to retain is :: Greater than 5, increase the last digit by 1 Ex) 56.87 g 56.9 g

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Rules for Rounding Numbers If the digit immediately to the right of the last significant figure you want to retain is :: Less than 5, do not change the last digit. Ex) 12.02 L 12.0 L

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Rules for Rounding Numbers If the digit immediately to the right of the last significant figure you want to retain is :: 5, followed by nonzero digit(s) increase the last digit by 1 Ex. 3.7851 seconds 3.79 seconds

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Rules for Rounding Numbers If the digit immediately to the right of the last significant figure you want to retain is :: 5, not followed by a nonzero digit and preceded by odd digit, increase the last digit by 1. Ex. 2.835 lbs 2.84 lbs

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Rules for Rounding Numbers If the digit immediately to the right of the last significant figure you want to retain is :: 5, not followed by a nonzero digit and preceded by even digit, do not change the last digit. Ex. 82.65 ml 82.6 ml

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