Question

Write whether the number $\frac{3717}{2^2\times 5^3\times 3}$ is terminating or non terminating. Justify.

Answer 1

We know,

If $x=\frac{p}{q}$ is a rational number, such that prime factorization of $q$ is of the form $2^n{5}^m$, where $n$ and $m$ are positive integers, then $x$ has a decimal expansion which terminates.

Then,

$x=\frac{3717}{2^2\times 5^3\times 3}=\frac{1239}{2^2\times 5^3}$ (fully reduced form)

Here, denominator, $q=2^2\times 5^3$,i.e. in the required form.

Therefore, $x=\frac{3717}{2^2\times 5^3\times 3}$ is terminating.