In a local election a candidate got 43.16% of the votes. Assuming normal rounding rules what's the minimum number of votes cast?

In general, given an interval

$$[a,b] \subset [0,1]$$

what's the smallest positive q such that there exist a p that p/q is in [a,b]?

Is there an easier way than checking every possibility from 1/2, 1/3,1/4,1/5,2/5 etc.

Question

In a local election a candidate got 43.16% of the votes. Assuming normal rounding rules what's the minimum number of votes cast?

In general, given an interval

$$[a,b] \subset [0,1]$$

what's the smallest positive q such that there exist a p that p/q is in [a,b]?

Is there an easier way than checking every possibility from 1/2, 1/3,1/4,1/5,2/5 etc.

beginnersmind · Answer

Bump and paging @Zarkon and @TuringTest. Hope it's ok