Express the following decimal in the rational form.$0 . \overline{4}$

Given :

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

To do :

We have to convert $0. \overline{4}$ to the rational form.

Solution :

$0. \overline{4}$

Let $x = 0.44444....$

Multiply both sides by 10.

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

$10x = 4.44444.....$

Therefore,

$10x-x = 4.444.... - 0.444.....$

$9x = 4$

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

Therefore,

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

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Updated on: 10-Oct-2022

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