 # Chapter 1.5 Uncertainty in Measurement. Exact Numbers Values that are known exactly Numbers obtained from counting The number 1 in conversions Exactly.

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Chapter 1.5 Uncertainty in Measurement

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

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

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

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

A measurement can be precise while still being inaccurate.

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

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

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

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

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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