Chapter 1 5 Uncertainty in Measurement Exact Numbers

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. 221 cm x 5. 2 cm = 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