Question

Write the condition to be satisfied by q so that a rational number has a non -terminating terminating decimal expansion.

Answer 1

Let x = \(\frac{p}{q}\) be a rational number, such that the prime factorization of q is not of the form 2ⁿ 5^m, where n, m are non - negative integers.

Then x has a decimal expansion which is non - terminating repeating (recurring).