Question

Write the condition to be satisfied by q so that a rational number \[\frac{p}{q}\] has a non-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 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 `2^mxx5^n`, where m and n are non-negative integers.