Question

Express $3.65\overline{1}$ in the from of $\frac{p}{q}$, where $p$ & $q$ are integers and $q\ne 0$.

Answer 1

Let $x=3.65\overline{1}$

$\Rightarrow x=\mathrm{3.651111...}$

$100x=\mathrm{365.1111...}$ .............. (1)

$1000x=\mathrm{3651.111...}$ ............. (2)

Subtract equation (1) from (2),

$1000x-100x=3286$

$900x=3286$

$x=\frac{3286}{900}$

$x=\frac{1643}{450}$