express 0.00352525252.... in pq form

$$\begin{gathered} Dear student, \\ Q. Express 4.0777... In the form of p/q. \\ Sol. Let x=4.07777.... \\ Therefore, x=4.0\overline{7} \\ There is one digit on the right side of the decimal point which is without bar. \\ So, multiply both sides by 10, so that only the repeating decimal is left of the decimal point. \\ Therefore, \\ 10x=40.\overline{7} \\ 10x=40.7777... \left(1\right) \\ Again multplying both sides of \left(1\right) by 10, we get \\ 100x=407.7777... \left(2\right) \\ Subtracting \left(1\right) from \left(2\right), we get, \\ 100x-10x=\left(407.7777\right)-\left(40.7777\right) \\ \Rightarrow 90x=367 \\ \Rightarrow x=\frac{367}{90} \\ Regards \end{gathered}$$