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

$\frac{23}{\left(2^3{5}^2\right)}$

Answer 1

If the denominator has factors in the form of $2^m\times 5^n$ then it has a terminating decimal expansion.

If the denominator has factors other than $2$ and $5$ then it has a non-terminating decimal expansion.

Here, $\frac{23}{\left(2^3{5}^2\right)}$ clearly, the denominator is in the form of $2^m\times 5^n$.

Hence, $\frac{23}{\left(2^3{5}^2\right)}$has a terminating decimal expansion.