repeating decimal

4.181818181818181... as a fraction

=4 2/11

4.181818181818181... as a fraction

$\begin{array}{|lrcll|} \hline (1) & 100 \times 4.\overline{18} &=& 418.\overline{18} \\ (2) & 1\times 4.\overline{18} &=& 4.\overline{18} \\ \hline (1)-(2) & 100 \times 4.\overline{18} - 1\times 4.\overline{18} &=& 418.\overline{18} - 4.\overline{18} \\ & 99\times 4.\overline{18} &=& 414 \\ & 4.\overline{18} &=& \frac{414}{99} \\ \hline \end{array}$