I would like to know if there is a way to find out the type of trailing decimals a fraction would create i.e. terminating or non terminating repeating decimals, without actually doing a division.
Like $14641/256 = 57.19140625$ which has a terminating decimal.
First put it in its lowest terms. Then the fraction terminates if and only if the denominator is in the form $2^a5^b$ (where either $a$ or $b$ may be zero).