Consider that it is mentioned that the number is a repeating decimal. So the cost value can be written as,
[tex]2.\bar{23}[/tex]
Let this number be 'x',
[tex]\begin{gathered} x=2.\bar{23} \\ x=2.232323\ldots \end{gathered}[/tex]
Multiply both sides by 100, since there are 2 digits repeating after the decimal,
[tex]\begin{gathered} 100x=223.\bar{23} \\ 100x=223.232323\ldots \end{gathered}[/tex]
Subtracting the equations,
[tex]\begin{gathered} 100x-x=223.\bar{23}-2.\bar{23} \\ 99x=223+0.\bar{23}-(2+0.\bar{23}) \\ 99x=223+0.\bar{23}-2-0.\bar{23} \\ 99x=221+0 \\ x=\frac{221}{99} \end{gathered}[/tex]
Thus, the fraction corresponding to the repeating decimal is 221/99.
And the corresponding mixed fraction can be evaluated as follows,
[tex]\frac{221}{99}=\frac{198+23}{99}=\frac{2(99)+23}{99}=2\frac{23}{99}[/tex]
Thus, the mixed fraction corresponding to the repeating decimal will be,
[tex]2\frac{23}{99}[/tex]
