The example of "16e2" would yield the interval [1550, 1650).  The smallest denominator possible is 1.  The smallest numerator that works with that denominator is 1550, but I don't like 1550/1 as the answer.

To cover these edge cases, I'd modify the optimization to be that we continue to seek the smallest denominator, but in the case that multiple numerators would give ratios within the computed interval then we choose the numerator among these that gives the ratio closest to the input value.