Express 3.565656..... in $\frac{p}{q}$ form.

Given :

The given number is 3.5656...

To do :

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

Solution :

Let the given number be x.

$x=3.5656....$

Multiply both sides by 10.

$10x=10(3.5656....)$

$10x=35.65656....$

Multiply both sides by 100.

$100(x)=100(3.5656....)$

$100x=356.5656.....$

Subtract x from 100x.

$100x-x=356.5656.... - 3.5656....$

$99x = 356-3$   (Since the digits after the decimals are same)

$99x=353$

$x=\frac{353}{99}$.

Therefore,

$3.5656...... = \frac{353}{99}$.

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Updated on: 10-Oct-2022

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