# UncertaintiesUncertainties

Absolute Uncertainties: The absolute uncertainty (usually called absolute error – but “error”
connotes “mistake”, and these are NOT mistakes) is the size of the range of values in which the
“true value” of the measurement probably lies
>If single readings have been taken then the uncertainty should be the smallest interval or
division on the measuring instrument. Consider the example below.
o Example: A metre rule is used to measure the length of a book. uncertainty in the
measuring instrument (the ruler) = ± 1mm length = (295 ± 1) mm
> The expression Percentage Uncertainty = (
Uncertainty/Average value ) x 100
o Referring back to the previous example about the ruler, The percentage uncertainty in
the length is % uncertainty = ± (1/295) x 100 = ±0.34%
> If multiple readings have been taken then half of the range of the readings will be the
uncertainty in the measured or calculated quantity.

Determining the uncertainty in time measurements using a stopwatch raises a few issues. Almost
all stopwatches will give times to one hundredth of a second, but humans clearly cannot operate
the watch to this accuracy. Human reaction time will give errors of (typically) 0.1s to 0.6s, which
are reasonable estimates of the uncertainty.
> Similar ideas apply to measurement of length, where parallax errors may make it difficult for
people to measure a length to the accuracy of the rule used.