Percentage Uncertainty

An uncertainty of ± 0.005 g sounds tiny, but whether it matters depends on how much you are weighing. The percentage uncertainty compares the uncertainty with the size of the measurement:percentage uncertainty = (uncertainty ÷ measured value) × 100Worked example 1: a 25.0 cm³ pipette has an uncertainty of ± 0.06 cm³.percentage uncertainty = (0.06 ÷ 25.0) × 100 = 0.24%Worked example 2: a balance has an uncertainty of ± 0.005 g. Compare weighing 0.250 g and 2.500 g.0.250 g: (0.005 ÷ 0.250) × 100 = 2%2.500 g: (0.005 ÷ 2.500) × 100 = 0.2%The same balance gives a ten times smaller percentage uncertainty when the mass is ten times larger. This is the key idea: for the same apparatus, measuring a larger quantity reduces the percentage uncertainty.Percentage uncertainty is the fairest way to compare the reliability of different measurements, such as a mass and a volume, because it has no units. It also shows which measurement contributes most to the overall uncertainty of a result, and so which piece of apparatus is worth improving.Percentage uncertainties are normally quoted to one or two significant figures, since the uncertainty itself is only an estimate.