the idea being, we first, move the repeating part to the left of the decimal point, by simply multiplying it by a power of 10, in this case, we need to move 318, so we need then 1000, 3 decimals, 3 zeros.
and we'll make the expression a variable, so let's do so first,
[tex]\bf \boxed{x=2.318318\overline{318}}\\\\
-------------------------------\\\\
\begin{array}{llll}
1000\cdot x&=&2318.318\overline{318}\\
&&2316+2.318318\overline{318}\\
&&2316+x
\end{array}\implies 1000x=2316+x
\\\\\\
999x=2316\implies x=\cfrac{2316}{999}\implies x=\cfrac{772}{333}\implies x=2\frac{106}{333}[/tex]
