$\mathrm{The} \frac{\mathrm{p}}{\mathrm{q}} \mathrm{form} \mathrm{of} \mathrm{the} \mathrm{number} 0.\overline{9} \mathrm{is}$

$$\begin{gathered} Let x=0.\overline{9} =0.999\cdots \\ 10x=10\times 0.999\cdots [\because Periodicity =1] \\ 10x=9.999... \_x=\_0.999... 9x =9.00... \\ 9x = 9 \\ x =\frac{9}{9}=1 \Rightarrow x =1 \\ \therefore 0.\overline{9} =1 \end{gathered}$$