Does the multiplication and division significant figures rule apply to unit conversions as well?

Question

My chemistry teacher told our class that answers to calculations that involve multiplication and division should be given to same number of significant figures as the factor, dividend or divisor with the lowest no. of sig.figs.

For example, to calculate the no.of moles of calcium in a pure 40g sample of calcium, the dividend (the mass) has 1 sig.fig. and the divisor (the molar mass) has 3 sig.figs. Hence the no. of mole sis given to 1 sig.fig.

40/40.1 = 1 mol of Calcium

Does this same rule apply to unit conversions? For example if I wanted to convert 12.4 milligrams to grams, I would need to divide 12.4 milligrams by 1000. 12.4 has 3 sig.figs. whereas 1000 has only 1 sig.fig. Does that mean the figure in grams must be given to 1 sig.fig?

Answer 1

In regards to the calcium situation, it depends on whether you measured 40g of calcium (which would be 2 sig. fig.), or 40g was the stated value (1 sig. fig.). Yes, the number of sig figs in your answer should equal the number of sig figs in the least accurate piece of data.

When converting units, the 1000 is taken as the exact value, i.e. it has infinite accuracy. Here, it is not considered, so the answer should have 3 sig fig from 12.4 (which is also why scientific notation is used to decrease ambiguity).