Question

Without actually performing the long division,state whether the following rational numbers will have a terminating decimal expansion or a non terminating repeating decimal expansion:
$\frac{13}{3125}$

Answer 1

A simplified fraction of the form $\frac{p}{q}$ has a terminating decimal expansion if and only if all the prime factors of $q$ are either 2 or 5.
Given: $q=3125=5^5$
As the only prime factor of the denominator is $5$, the decimal expansion will be terminating.