Express each of the following decimals in the form $\frac{p}{q}$:
$ 0.4 \overline{7} $

Given:

The given decimal number is \( 0 . 4\overline{7} \).

To do:

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

Solution:

$0. 4\overline{7}$

Let $x = 0.47777....$

Multiply both sides by 10.

$10x = 10(0.47777....)$

$10x = 4.7777.....$

Multiply both sides by 100.

$100x = 100(0.47777....)$

$100x = 47.7777.....$

Therefore,

$100x-10x = 47.7777.... - 4.7777.....$

$90x = 43$

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

Therefore,

$0. 4\overline{7}$ in $\frac{p}{q}$ form is $\frac{43}{90}$. 

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Updated on: 10-Oct-2022

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