Uncertainty in Measurement

Precision and Accuracy Precision – Measure of how close individual measurements agree with one another A standard deviation tells someone how precise you were during a laboratory. Accuracy – How close individual measurements agree with the “true” value.

Significant Figures There is always uncertainty in the last digit of any quantity that we report. Significant Figures – All digits of a measured quantity The number of digit reported represent the number of significant figures a number has

Determining the Number of Sig Figs When looking at a number we need to determine how many sig figs it has. The most important rule is that all nonzero digits in any measurement are significant There are special rules for zeros: Zeros between nonzero digits are always significant. For example, 1005 has 4 sig figs. Zeros at the beginning of a number are never significant. For example, 0.005 has 1 sig fig. Zeros at the end of a number are significant only if there is a decimal. For example, 3.0 has 2 sig figs, but 30 has 1 sig fig.

A Note on Scientific Notation Recall that we can write a number like 10,300 in scientific notation as 1.03 x 104 This number would have 3 sig figs We only count the numbers. We do not count the exponential term.

Class Example Determine the number of significant figures in the following numbers: 6.3050 cm 601 kg 0.054 s 0.0105 L 7.0500 x 10-3 m3 400 g

Sig Figs for Calculations For any calculation, which ever measurement we are least certain about determines the number of sig figs in the answer Determine sig figs only after a calculation is complete.

Sig Fig for Addition/Subtraction When you add/subtract numbers, the answer has the same number of decimal places as the number with the least decimal places. Round off to one decimal place since 83.1 has the least number of decimal places! Final answer you report is 104.8

Sig Figs for Multiplication/Division When you multiply or divide numbers, the answer has the same number of sig figs as the number with the fewest sig figs. 4 sig figs 2 sig figs, so the answer needs 2 sig figs 32 cm2

Class Example Report the answers to these functions with the correct number of sig figs: 1. 4.5 x 40.234 = 2. 23.98 + 13 = 3. 4. 40 x 3.25 =