Uncertainty is based on the fact that it is impossible to measure the exact precision of something when particles and subatomic particles are constantly moving. The uncertainty in the measurements we take are the results of the uncertainty of the instruments we use or the skills (or lack there of) of the people taking the measurements. There are two ways to express uncertainty:
Absolute Uncertainty: Expressed (with the correct number of sig figs!) in the same units as the measurements themselves
Ex) The measurement of 5.9 cm has an absolute uncertainty of ± 0.050 cm
My temperature is 107.7° F with an absolute uncertainty of ± 0.5000 ° F (please help)
Relative Uncertainty: Expressed (with the correct number of sig figs!) as a percentage
Ex) The measurement of 5.9 cm has a relative uncertainty of ± 8.5%
My temperature is 107.7° F with a relative uncertainty of ± 0.4643% (I'm quite sick)
Ex) The measurement of 5.9 cm has an absolute uncertainty of ± 0.050 cm
My temperature is 107.7° F with an absolute uncertainty of ± 0.5000 ° F (please help)
Relative Uncertainty: Expressed (with the correct number of sig figs!) as a percentage
Ex) The measurement of 5.9 cm has a relative uncertainty of ± 8.5%
My temperature is 107.7° F with a relative uncertainty of ± 0.4643% (I'm quite sick)
Determining Absolute Uncertainty
1) Sometimes the uncertainty is written on the instrument itself, so you can use that.
2) When the instrument does not indicate a specific uncertainty, the uncertainty is equal to one half of the smallest measurement provided by the instrument
Ex) A ruler, where the smaller measurement is a millimetre (. 1 cm), the absolute uncertainty would be ± 0.5 mm (.05 cm)
Ex) A thermometer, where the smallest measurement is a degree, the absolute uncertainty would be ± 0.5 °
Determining Relative Uncertainty
This should be a crime it's so easy. Simply divide the absolute uncertainty by your measurement and multiply by 100
Ex: The ruler: ( 0.05 cm / 5.9 cm ) x 100 = ± 8.5%
My fever: ( 0.5 ° / 107.7 ° ) x 100 = ± 0.4643%
1) Sometimes the uncertainty is written on the instrument itself, so you can use that.
2) When the instrument does not indicate a specific uncertainty, the uncertainty is equal to one half of the smallest measurement provided by the instrument
Ex) A ruler, where the smaller measurement is a millimetre (. 1 cm), the absolute uncertainty would be ± 0.5 mm (.05 cm)
Ex) A thermometer, where the smallest measurement is a degree, the absolute uncertainty would be ± 0.5 °
Determining Relative Uncertainty
This should be a crime it's so easy. Simply divide the absolute uncertainty by your measurement and multiply by 100
Ex: The ruler: ( 0.05 cm / 5.9 cm ) x 100 = ± 8.5%
My fever: ( 0.5 ° / 107.7 ° ) x 100 = ± 0.4643%