Express each of the following decimals in the form $\frac{p}{q}$:$ 0 . \overline{4} $

Given:

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

To do:

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

Solution:

$0. \overline{4}$

Let $x = 0.4444....$

Multiply both sides by 10.

$10x = 10(0.4444....)$

$10x = 4.4444.....$

Therefore,

$10x-x = 4.4444.... - 0.4444.....$

$9x = 4$

$x = \frac{4}{9}$

Therefore,

$0. \overline{4}$ in $\frac{p}{q}$ form is $\frac{4}{9}$.

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Updated on: 10-Oct-2022

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