Question

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non terminating repeating decimal expansion:
$\frac{23}{2^3{5}^2}$

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: $q=2^3{5}^2$
As the only prime factors of the denominator are $2$ and $5$, the decimal expansion will be terminating.