Question

Without actually performing long division state whether the following rational number will have a terminating decimal expansion or a non - terminating repeating decimal expansion 427/625

Answer 1

yes it is terminating decimal
because x/2^n×5^m where x is any number is terminating decimal only
427/625=427/2^0×5^4

Answer 2

It can be possible to determine the decimal expansion is terminating or non terminating if the denominator have only 2 and 5 factors. Therefore, 427/625 it has denominator is 625 whose have only 5 has factor so it is a terminating decimal.