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Chapter 1.5 Uncertainty in Measurement

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Exact Numbers Values that are known exactly Numbers obtained from counting The number 1 in conversions Exactly 2.54 cm in an inch

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Inexact Numbers Values with some uncertainty All numbers obtained by measurement Human error Equipment limitations Counting very large number of objects

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Precision Term used for describing uncertainties Measures how closely individual measurements agree with one another

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Accuracy Term used with uncertainties Measure of how closely individual measurements agree with the correct or true value

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A measurement can be precise while still being inaccurate.

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Significant Figures Measured quantities are generally reported in such a way that only the last digit is uncertain. Think of a thermometer All digits, including the last one, are considered significant figures

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Rules for Sig Figs All nonzero digits are significant »678 has 3 sig figs Zeros between nonzero digits are significant »2034 has 4 sig figs Leading zeros are never significant »0.00006 has 1 sig fig Zeros at the end of a number are significant if the number contains a decimal point »0.003000 has 4 sig figs »980 has 2 sig figs

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Sig Figs in Calculations Least certain measurement limits certainty of final answer RULE 1: In multiplication and division- sig figs of the answer should be the same as the measurement with the fewest sig figs 6.221cm x 5.2cm = 32.3492 cm 2 = 32 cm 2

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RULE 2: For addition and subtraction- final answer has the same number of decimal places as the measurement with the fewest decimal places. 20.42 + 1.322 + 83.1 = 104.842 = 104.8

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Intermediate Answers Retain at least one additional digit past the sig figs. If using a calculator, enter numbers one after another

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