question_answer

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:

52.0521

\[\Rightarrow \]               \[52.0521=\frac{520521}{10000}\]

Yes, it is rational number.

where \[q=10000={{2}^{4}}\times {{5}^{4}}\]

The given decimal expression is a terminating decimal as the factors of q consist only 2 and 5.