Question

Express $0.4\overline{7}$ in the form of $\frac{p}{q}$.

Answer 1

Let $x=0.4\overline{7}$

$x=\mathrm{0.477.......}\left(i\right)$

on multiplying equation $\left(i\right)$ by $10$, we get

$10x=10\times \mathrm{0.477....}$

$10x=\mathrm{4.777......}\left(ii\right)$

Again, on multiplying eq. $\left(ii\right)$ by $10,$ we get

$100x=\mathrm{47.777......}\left(iii\right)$

Subtract eq. $\left(ii\right)$ from eq. $\left(iii\right),$ we get

$100x-10x=\mathrm{47.777......}-\mathrm{4.777....}$

$\Rightarrow 90x=43$

$\Rightarrow x=\frac{43}{90}$ ( $\frac{p}{q}$ form )

Therefore, $x=0.4\overline{7}=\frac{43}{90}$