Express each of the following decimals in the form $\frac{p}{q}$:
$ 125. \overline{3} $.

Given:

The given decimal number is \( 125 . \overline{3} \).

To do:

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

Solution:

$125. \overline{3}$

Let $x = 125.33333....$

Multiply both sides by 10.

$10x = 10(125.3333....)$

$10x = 1253.3333.....$

Therefore,

$10x-x = 1253.3333.... - 125.3333.....$

$9x = 1128$

$x = \frac{1128}{9}$

$x=\frac{3\times376}{3\times3}$

$x=\frac{376}{3}$

Therefore,

$125. \overline{3}$ in $\frac{p}{q}$ form is $\frac{376}{3}$. 

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Updated on: 10-Oct-2022

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