Physics
Physics
Problem
Explain why percentage error, rather than absolute error, is more appropriate for comparing the precision of two measurements that have different magnitudes or units.Intuitive explanation
Percentage error removes the bias of scale—a 1 cm error means something very different when measuring a pencil versus a building. By dividing absolute error by the true value, you normalize the mistake to what you were actually trying to measure, making it fair to compare wildly different experiments. This is why scientists always report relative uncertainty: it tells you whether your technique was sloppy or skillful, independent of what you happened to be measuring.
Intuitive explanation
Percentage error removes the bias of scale—a 1 cm error means something very different when measuring a pencil versus a building. By dividing absolute error by the true value, you normalize the mistake to what you were actually trying to measure, making it fair to compare wildly different experiments. This is why scientists always report relative uncertainty: it tells you whether your technique was sloppy or skillful, independent of what you happened to be measuring.