1 / 7

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.

agalia
Download Presentation

Uncertainty in Measurements

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related