Express each of the following decimals in the form $\frac{p}{q}$:
$ 4. \overline{7} $

Given:

The given decimal number is \( 4 . \overline{7} \).

To do:

We have to express the given decimal in $\frac{p}{q}$ form.

Solution:

$4. \overline{7}$

Let $x = 4.7777....$

Multiply both sides by 10.

$10x = 10(4.7777....)$

$10x = 47.7777.....$

Therefore,

$10x-x = 47.7777.... - 4.7777.....$

$9x = 43$

$x = \frac{43}{9}$

Therefore,

$4. \overline{7}$ in $\frac{p}{q}$ form is $\frac{43}{9}$. 

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Updated on: 10-Oct-2022

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