Express each of the following decimals in the form $\frac{p}{q}$:$ 0 . \overline{621} $

Given:

The given decimal number is \( 0 . \overline{621} \).

To do:

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

Solution:

$0. \overline{621}$

Let $x = 0.621621....$

Multiply both sides by 10.

$10x = 10(0.621621....)$

$10x = 6.21621......$

Multiply both sides by 100.

$100x = 100(0.621621....)$

$100x = 62.1621621.....$

Multiply both sides by 1000.

$1000x = 1000(0.621621....)$

$1000x = 621.621621.....$

Therefore,

$1000x-x = 621.621621.... - 0.621621.....$

$999x = 621$

$x = \frac{621}{999}$

$x=\frac{27\times23}{27\times37}$

$x=\frac{27}{37}$

Therefore,

$0. \overline{621}$ in $\frac{p}{q}$ form is $\frac{27}{37}$.   

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Updated on: 10-Oct-2022

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