Question

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

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^mxx5^n`, where m and n are non-negative integers.