Question

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

Answer 1

The rational number $\frac{p}{q}$ where p and q are co-prime q will have a ferminating decimal expansion only if the prime factorisation of q is of the form $2^n.5^m$, where n and m are non-negative integers.