Question

Express 0.56125 in the form $\frac{p}{q}$, where $p$ and $q$ are co-prime and also $q$ in the form $2^n\times 5^m$.

Answer 1

We can write $0.56125$ as follow

$p÷q=56125÷100000$

also $56125$ can be written as $5\times 5\times 5\times 449$

and $100000$ as $2\times 2\times 2\times 2\times 2\times 5\times 5\times 5\times 5\times 5$

If you divide $p$ by $q$ then you will get $\left(449\right)÷(2\times 2\times 2\times 2\times 2\times 5\times 5)$

So $q$ can be written as $2^5\times 5^2$