Section 1 4 Uncertainty in Measurement Exact Numbers

Section 1. 4 Uncertainty in Measurement

Exact Numbers • Values with no uncertainty • Numbers obtained from counting • The numbers in conversions

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

Sig Figs Rules 1. All nonzero digits are significant 678 has 3 2. Zeros between nonzero digits are significant 2034 has 4 3. Leading zeros are never significant 0. 00006 has 1 4. Trailing zeros are significant if the number contains a decimal point 0. 003000 has 4 980 has 2

Sig Figs in Calculations • RULE 1: 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: addition and subtraction- final answer has the same number of decimal places as the measurement with the fewest decimal places. • 20. 42 m + 1. 322 m + 83. 1 m = 104. 842 m = 104. 8 m

Intermediate Answers • If you are staying within the same rule: Enter numbers in the calculator and do not round until the end • If you are switching between rules 1 and 2: you MUST round like a final answer before the switch!