Write $0.4\overline{7}$ in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q≠0$.

Given: A number $0.4\overline{7}$.

To do: To write the given number in the form of $\frac{p}{q}$.
 

Solution:

Let $x=0.477777$ ...... $( i)$

On multiplying $( i)$ by $10$,

$10x=4.777$ ...... $( ii)$

On subtracting $( i)$ from $( ii)$,

$( 10x-x)=( 4.777)-( 0.4777)$

$\Rightarrow 9x=4.3$

$\Rightarrow x=\frac{4.3}{9}=\frac{43}{90}$

Thus, $x=\frac{43}{90}$

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Updated on: 10-Oct-2022

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