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......!!!!
Express as a common fraction.
$$\left\begin{array}{rcl}
10 \times 3.\overline{7} &=& 37.\overline{7} \\
1 \times 3.\overline{7} &=& 3.\overline{7} \\
\hline
\end{array} \right\} -$$
$$\begin{array}{rcl}
(10-1)\times 3.\overline{7} &=& 37.\overline{7} - 3.\overline{7} \\
9 \times 3.\overline{7} &=& 34 \\
9 \times 3.\overline{7} &=& 34 \qquad | \qquad : 9 \\
3.\overline{7} &=& \dfrac{34}{9}
\end{array}$$