Measurement: Reliability, Accuracy, and Precision

1. Section 2.3 Measurement Reliability

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

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

4. Measurements can be precise while still being inaccurate.

6. Percent Error • Percent of the accepted value an error represents • Ratio of an error to an accepted value Percent Error = error x 100 accepted value

7. Significant Figures

8. 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

9. Rules for Sig Figs • All nonzero digits are significant • Zeros between nonzero digits are significant • 203 has 3 sig figs • Zeros at the beginning of a number are never sig figs • 0.0006 has 1 sig fig • Zeros at the end of a number are significant if the number contains a decimal point • 0.0300 has 3 sig figs • 200 has 1 sig fig

10. 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 cm2 = 32 cm2

11. 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

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