It is given that the number is x=-2.2727272727...
This is a recurring decimal so multiply by 100 to get:
[tex]100x=-227.27272727\ldots[/tex]Subtract the two equations to get:
[tex]\begin{gathered} 100x-x=-227.272727\ldots+2.27272727\ldots \\ 99x=-225 \\ x=-\frac{225}{99} \end{gathered}[/tex]Hence the fractional value is given by:
[tex]-2.27272727\ldots=\frac{-225}{99}[/tex]