If 1.525252.... is converted to a fraction, then what is the sum of its numerator and denominator?

Given :

Given decimal number is 1.525252....

To find :

We have to convert it into a fraction.

Solution :

Let x = 1.525252...

Multiply it by 100 on both sides.

This implies,

100x = $100\times1.525252.....$

100x = 152.525252....

Subtract x from 100x to get,

$100x-x=152.525252.....-1.525252.....$

99x = 151

x=$\frac{151}{99}$

The required fraction is $\frac{151}{99}$.

Therefore, the sum of the numerator and denominator = $151+99=250.$  

Tutorialspoint

Updated on: 10-Oct-2022

39 Views

Kickstart Your Career

Get certified by completing the course

Get Started