Significant figure question

Question

The size of an rectangular sheet of paper is found by measuring as accurately as possible, $8.45$ inches by $11.03$ inches. What is the area, to the same accuracy, in square inches?

Answer is $93.20$, not $93.2$

I thought since $8.45$ only had $3$ significant figures the answer should also only have $3$ significant figures? What's going on?

Answer 1

I agree with you. Significant figures are an approximate way of doing error propagation, and you have followed the usual rule. If we do a true error analysis assuming the error in measurement can be half the last place, the minimum area is $8.445\cdot 11.025\approx 93.106$ and the maximum is $8.455 \cdot 11.035 \approx 93.301$, so $93.2\pm 0.1$ is a reasonable representation of what you know. Certainly $93.20$ gives the impression you know it more accurately than you do in this model.

Answer 2

The measurements are correct to $2$ places of decimal fractions, so the answer should be written to that accuracy as well.