0.242424242424242424242424...........................................................

Level pending

The number 0.242424....... can be expressed as x/y. Where x and y both are coprime positive integers. What is the value of x+y ?


The answer is 41.

Raiyun Razeen by Raiyun Razeen , 22, Bangladesh

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Budi Utomo
Jan 6, 2014

24/99 = 8/33 ---> 8 + 33 = 41

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Lee Wall
Jan 13, 2014

Let x = 0.242424... Then 100x = 24.242424... Therefore, 100x - x = 99x = 24, so x is 24/99 = 8/33, yielding an answer of 8 + 33 = 41.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Asad Haider
Jan 8, 2014

We will use a geometric progression this would be as follows: 0.24+0.0024+0.000024........ the common ratio=0.01 so the sum to infinity=0.24/(1-0.01)=8/33 both 8 and 33 are co prime and their sum =41

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...