Originally Posted by Val
The mathematically correct answer (admittedly a bit absurd on its face) is to use one significant digit and round accordingly

Well, you're right about how to calculate significant figures. But the idea of significant figures itself is merely a notational convention, not a mathematical truth.

Think about it: for a number like 5,000 to always be "more correct" under conditions of uncertainty than, say, 5,136 -- purely in virtue of its having all those zeros -- would have to mean that there was something magical about numbers that happen to end in zeros in base-10 notation.

The purpose of using numbers with all those zeros is merely to signal to others something about the precision of the estimate. It does not make the number a better estimate. It does not make the answer more correct.

But the fact that we can get into a friendly argument about this at such a high level of abstraction just shows how pedagogically absurd the question is for that age-group!