Question

How do you convert 3.16 (6 repeating) to a fraction?

Answer 1

Suppose $x=3.1\overline6$. Then $10x=31.\overline6$, and $100x=316.\overline6$.

Now,

$100x-10x=316.\overline6-31.\overline6=316-31$

$\implies90x=285$

$\implies x=\dfrac{285}{90}=\boxed{\dfrac{19}6}$