Convert the following into a vulgar fraction :

${0.\overline{34}}$

Let $x = 0.\overline{34}$. Then,

x = 0.343434… (i)

⇒ 100x = 34.343434… (ii)

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

$99x = 34 \\[1em] \Rightarrow x = \dfrac{34}{99}$

Hence, $0.\overline{34} = \dfrac{34}{99}$