Express as a common fraction.

Express  as a common fraction.

$$\left\begin{array}{rcl} 10 \times 3.\overline{7} &=& 37.\overline{7} \\ 1 \times 3.\overline{7} &=& 3.\overline{7} \\ \hline \end{array} \right\} -$$

$$\begin{array}{rcl} (10-1)\times 3.\overline{7} &=& 37.\overline{7} - 3.\overline{7} \\ 9 \times 3.\overline{7} &=& 34 \\ 9 \times 3.\overline{7} &=& 34 \qquad | \qquad : 9 \\ 3.\overline{7} &=& \dfrac{34}{9} \end{array}$$

3.7777......  =  3 + 77/99  = 3 +7/9  = 34/9

I edited this one for a previous mistake......!!!!