find two different rational numbers whose decimal representation begins 0.232323232

Question

I need to rational numbers if possible! 

Answer 1

if this is a repeating decimal, then...

n=0.2323232323...

100n=23.23232323...

 

100n=23.23232323...

-

       n=0.23232323...

99n=23

n=23/99

there is only one number equal to 0.2323232323...

you can use 46/198 but it's the same as 23/99

Answer 2

The repeating decimal  0.232323232323....

 

Let that number equal x

 

Then 100x = 23.23232323....

 

                = 23 + x

 

Solve for x to get 23/99

 

In the case of .232323232 exactly, multiply by 1,000,000,000 to get 232,323,232. the fraction of the latter number divided by one billion is your answer....this happens to reduce by a factor of 32 to get 7,260,101/31,250,000