Suppose [tex]x=3.1\overline6[/tex]. Then [tex]10x=31.\overline6[/tex], and [tex]100x=316.\overline6[/tex].
Now,
[tex]100x-10x=316.\overline6-31.\overline6=316-31[/tex]
[tex]\implies90x=285[/tex]
[tex]\implies x=\dfrac{285}{90}=\boxed{\dfrac{19}6}[/tex]
