Suppose someone tells you "0.25 of the balls in this jar are blue". What is the total number of balls in the jar? You cannot know for sure, but you can tell that the number is at least 4. Why? because if there were 2 then the fraction could donly be 0 or 0.5 or 1, and if there were 3 then the fraction could only be 0 or 0.333... or 0.666... or 1 - in any case it could not be 0.25.
What if that someone tells you "0.14 of the balls in this jar are blue"? If the fraction is accurate, then the smallest possible total is 50 (with 7 blues, since 7/50=0.14), but it is also possible that the someone rounded the actual fraction to 2 significant digits. In this case, the smallest possible total is 7 (with 1 blue).
My question is: what is an algorithm that takes a finite decimal fraction with $k$ digits, $0.d_1 d_2\ldots d_k$, and returns the smallest possible integer $t$ such that, for some $b<t$, the fraction $b/t$ rounded to $k$ significant digits equals $0.d_1 d_2\ldots d_k$?