What is the rule for determining the number of significant figures in density?

Answer 1

Suppose the mass is m, to an accuracy such that it lies between m-a and m+a.Suppose the volume is v, to an accuracy such that it lies between v-b and v+b.

Calculate

d1 = (m-a)/(v+b)

and

d2 = (m+a)/(v-b).

Then the number of sig figs in the density is the number of digits to which the rounded versions of d1 and d2 agree.

The density may not have any significant figures, in which case simply use the first digit m/v.

So suppose the mass is 20 grams, accurate to the nearest gram (a = 0.5 g), and that the volume is 7 ml with an accuracy of 0.1 ml (b = 0.05 ml).

Then d1 = 19.5/7.05 = 2.7660 and d2 = 2.9496 (approx)

To 2 sig figs d1 = 2.8 and d2 = 2.9 are unequal but to 1 sf, d1 = 3 = d2.

So that appropriate number of sf is 1.