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 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, where m and n are non-negative integers.