Convert the following into a vulgar fraction :

${2.\overline{13}}$

Let x = $2.\overline{13}$.

Then,

x = 2.131313… (i)

⇒ 100x = 213.131313… (ii)

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

$99x = 211 \\[1em] \Rightarrow x = \dfrac{211}{99} \\[1em] \Rightarrow x = 2\dfrac{13}{99}$

Hence, $2.\overline{13} = 2\dfrac{13}{99}$