Convert the following into a vulgar fraction :

${0.\overline{6}}$

Let $x = 0.\overline{6}$. Then,

x = 0.6666… (i)

⇒ 10x = 6.6666… (ii)

On subtracting (i) from (ii), we get:

$9x = 6 \\[1em] \Rightarrow x = \dfrac{6}{9} = \dfrac{2}{3}$

Hence, $0.\overline{6} = \dfrac{2}{3}$