A student checks the purity of a water sample by determining its density (mass per unit volume) at 25°C. (The density of pure water is listed as 0.9970 g/cm3 in a handbook.) The student measures 25 cm3 of the sample from a cylinder and determines its mass to be 25.624 g. What should be reported for the density?
Solution
The precision of the density determination is limited by that of the volume measurement, which has only two significant figures.
density = mass/volume = 25.624 g / 25 cm3 = 1.0 g/cm3
The five significant figures in the mass measurement were wasted; the mass measurement may just as well have been performed on a balance that weighed to the nearest gram.
