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 has a non-terminating decimal expression.

For the terminating decimal expression, we should not have a multiple of 10 in the denominator.

Hence, the prime factorization of q must not be of the form, where m and n are non-negative integers.