Question

State whether the real number 52.0521 is rational or not. If it is rational express it in the form $\frac{p}{q},$ where p, q are co - prime, integers and $q\ne 0.$ What can you say about prime factorisation of q?

Answer 1

Yes $52.0521$ is rational as the given decimal expression is a terminating decimal rational.
$\Rightarrow 52.0521=\frac{520521}{10000}$
where $q=10000=2^4\times 5^4$
Prime factors of q consist only 2 and 5.