# 3.  Express the following in the form $\frac{p}{q}$ , where p and q are integers and q ≠ 0.(ii)     $0.4\bar{7}$

G Gautam harsolia

We can write $0.4\overline7$ as

$\Rightarrow 0.4\overline7 = \frac{4}{10}+ \frac{0.777..}{10}$             -(i)

Now,

Let $x = 0.\overline7= 0.7777....$             -(ii)

Now, multiply by 10 on both sides

$10x= 7.7777...$

$\Rightarrow 10x = 7 + x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(using \ (ii))$

$\Rightarrow 9x = 7$

$\Rightarrow x = \frac{7}{9}$
Now, put the value of x in equation (i). we will get

$\Rightarrow 0.4\overline7 = \frac{4}{10}+ \frac{7}{10\times 9}= \frac{4}{10}+ \frac{7}{90} = \frac{36+7}{90} = \frac{43}{90}$

Therefore,  $\frac{p}{q}$  form of  $0.4\overline7$  is  $\frac{43}{90}$

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