Question

Write the condition to be satisfied by q so that a rational number \[\frac{p}{q}\] has a terminating decimal expansion.

Answer 1

We need to find the condition to be satisfied by q so that a rational number `p/q` has a terminating decimal expression.

For the terminating decimal expression, we should have a multiple of 10 in the denominator.

Hence, the prime factorization of q must be of the form `2^m xx 5^n`, where m and n are non-negative integers.