Uncertainty in Measurement Accuracy vs. Precision

Uncertainty Basis for significant figures All measurements are uncertain to some degree The last estimated digit represents the uncertainty in the measurement Each Person may estimate a measurement differently Person 1 6.63mls Person 2 6.64mls Person 3 6.65 mls

Rules for Counting Significant Figures 1. Non-zeros always count as significant figures: 3456 has 4 significant figures

Rules for Counting Significant Figures 2. Leading zeroes do not count as significant figures: 0.0486 has 3 significant figures

Rules for Counting Significant Figures 3. Captive zeroes always count as significant figures: 16.07 has 4 significant figures

Rules for Counting Significant Figures 4. Trailing zeros (or zeros after a non-zero digit) are significant only if the number contains a written decimal point: 9.300 has 4 significant figures has 1 significant figure 100. has 3 significant figures

Sig Fig Practice #1 How many significant figures in the following? 5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs These all come from some measurements 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000 mL  2 sig figs

Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. 6.8 + 11.934 = 18.734  18.7 (3 sig figs)

Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. 6.38 x 2.0 = 12.76  13 (2 sig figs)

Precision vs. Accuracy Precision- how repeatable Precision is determined by the uncertainty in the instrument used to take a measurement. So . . . The precision of a measurement is also how many decimal places that can be recorded for a measurement. 1.476 grams has more precision than 1.5 grams. Accuracy- how correct - closeness to true value.

Measurement Errors Random error - equal chance of being high or low- addressed by averaging measurements - expected Systematic error- same direction each time Want to avoid this Bad equipment or bad technique. Better precision implies better accuracy You can have precision without accuracy You can’t have accuracy without precision (unless you’re really lucky).

Percent Error Percent Error compares a measured value to its true value. It measures the accuracy in your measurement. %Error = Measured value – accepted value x 100 accepted value

Average Deviation Average Deviation – measures the repeatability (or precision) of your measurements. Deviation = measured value – average value You calculate the deviation for each measurement and then take the average of those deviations to get the “Average Deviation” Measurement is then reported as the average + average deviation For example: 6.64mls + 0.01mls

Each Person may estimate a measurement differently Deviation Person 1 6.63mls 0.01 mls Person 2 6.64mls 0.00 mls Person 3 6.65 mls 0.01 mls Average 6.64 mls +/- 0.01 mls