Express each of the following decimals in the form $\frac{p}{q}$:$ 0 . \overline{37} $

Given:

The given decimal number is \( 0 . \overline{37} \).

To do:

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

Solution:

$0. \overline{37}$

Let $x = 0.3737....$

Multiply both sides by 10.

$10x = 10(0.3737....)$

$10x = 3.737.....$

Multiply both sides by 100.

$100x = 100(0.3737....)$

$100x = 37.3737.....$

Therefore,

$100x-x = 37.3737.... - 0.3737.....$

$99x = 37$

$x = \frac{37}{99}$

Therefore,

$0. \overline{37}$ in $\frac{p}{q}$ form is $\frac{37}{99}$. 

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Updated on: 10-Oct-2022

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