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Uncertainty in Measurements

Uncertainty in Measurements. All measurements are limited by the instruments used to make them . (some uncertainty). Depends on the quality with which a measurement is made and on the precision and accuracy of the measurement Signified by + The last number is UNCERTAIN. 1.

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Uncertainty in Measurements

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  1. Uncertainty in Measurements • All measurements are limited by the instruments used to make them. (some uncertainty). • Depends on the quality with which a measurement is made and on the precision and accuracy of the measurement • Signified by + • The last number is UNCERTAIN. 1

  2. Uncertainty in Measurements *ALL MEASUREMENTS HAVE UNCERTAINTY Analog (thermometer, graduated cylinders, etc.) *uncertainty is +/- 0.5 of the estimated decimal place. e.g.-10 mL graduated cylinder, 1 mL marks  estimate 0.5 mL (7.5+/-0.5mL, 0.5 is estimated) Digital (thermometer, balance, etc.) *uncertainty is +/- 1 in the last decimal place. e.g.-an electronic balance measures down to 0.01 g. (4.56+/-0.01g*, 0.01 is estimated) *as reported as tolerance by manufacturer. 2

  3. Uncertainty in Measurements Addition/Subtraction: • The maximum uncertainty is the sum of the individual uncertainties. • The rule for both Add/Sub is to add the absolute uncertainties. total 30.200 +0.08-g However, using “the rules”: 30.20 +0.08-g • (Dumb People Are Stupid = Decimal Place, Add/Subtract) 3

  4. Uncertainty in Measurements Multiplication/Division: • If uncertainties are to be multiplied or divided then % uncertainties have to be used (to account that physical quantities will have different units. • The maximum uncertainty is the sum of the % uncertainties for each individual quantities. 4

  5. Uncertainty in Measurements Multiplication/Division (cont.): Problem: 2.4 + 0.2 cm x 1.3 + 0.2 cm • Steps: • 1. Take each (individual) uncertainty 2.4 + 0.2 cm  0.2 • 2. divide it by the given value (given measurement) 0.2/2.4 = 0.083 • 3. multiply by 100 to obtain % 0.083 x 100 = 8.3% Do the same for the other number(s): (0.2/1.3) x 100 = 15.4% 5

  6. Uncertainty in Measurements Multiplication/Division (cont.): • 4. % uncertainties can then be added. 8.3% +15.4% 23.7% • 5. Once desired math function is done on the measurement, 2.4 x 1.3 = 3.12 (+ 23.7%) - 6. the % uncertainty is converted back to a number. 3.12 x 23.7% = 0.739 • 7. The uncertainty is joined with the calculated value and both are adjusted to the appropriate Significant Figures. 3.12 + 0.739  (sig figs) 3.1 + 0.7 cm 6

  7. Uncertainty in Measurements (the whole process) • Ex. 2.4 + 0.2 cm  0.2/2.4 = 0.083 x 100 = 8.3% 1.3 + 0.2 cm  0.2/1.3 = 0.154 x 100 = 15.4% 23.7% 2.4 x 1.3 = 3.12 + 23.7% 3.12 x 23.7% = 0.739 3.12 + 0.739  (sig figs) 3.1 + 0.7 cm • (My Dad Sells Fireworks = Multiply/Divide, Sig. Fig.) 7

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