Question

Write the following rational number in $\frac{p}{q}$ form $0.\overline{37}$.

Answer 1

$$\begin{array}{c}0.3informof\frac{p}{q}\\ letx=0.37...........eq\left(i\right)\\ Multiplyby10bothside\\ 10x=3.37............eq\left(ii\right)\\ subtract\left(ii\right)from\left(i\right)\\ 9x=(3.37-0.37)\\ 9x=3\\ x=\frac{1}{3}\end{array}$$