It is true that we cannot measure things exactly (unless we're robots...) however that doesn't mean we can't give it our best. Here are a few notes we took last class, explaining the uncertainties of measurements.
- Precision: How reproducible a measurement is compared to other similar measurements.
- Accuracy: How close the measurement (or average measurement) comes to the accepted or real value.
Measurement and Uncertainty
- No measurement is exact. Only best estimates which has a some degree of uncertainty.
-Only when we count do we get an exact number (ex: There are 28 students in this class. There cannot be
28.5... that would be just weird.)
Absolute Uncertainty
-Uncertainty is expressed in the units of measurement not ratio
Method 1: Make 3 measurements, calculate the average (Make sure to take out the measurements that are "different" from the others. Ex: 2.3, 2.32, 2.46, 2.33). The absolute uncertainty = largest difference between the average and lowest/highest reasonable measurement.
Method 2: Determine the uncertainty of each instrument. Always measure to the best precision that you can. Therefore you should estimate to a fraction 0.1 of the smallest segment on the instrument scale. (On your ruler the smallest division = 1mm. Your best precision should be to break this into 10 equal pieces.)
Relative Uncertainty and Significant Figures
-Relative uncertainty = absolute uncertainty divided by estimated measurement
-Relative uncertainty can be expressed
- In percent %
- or using significant figures (sig. figs.)
- The number of sig. figs. = relative uncertainty: The last digit in a measurement is uncertain as it could be one digit higher or lower very easily.
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