SOLUTION: My teacher gave us a problem not in our textbook. For a repeating number 3.181818..., what is the way to find it's ratio if x equals .1818... I've tried dividing 18 by 1

Algebra ->  Real-numbers -> SOLUTION: My teacher gave us a problem not in our textbook. For a repeating number 3.181818..., what is the way to find it's ratio if x equals .1818... I've tried dividing 18 by 1      Log On


   

Question 102905: My teacher gave us a problem not in our textbook.
For a repeating number 3.181818..., what is the way to find it's ratio if x equals .1818...
I've tried dividing 18 by 100 and simplyfying it to 9/50, but can't get to the answer which is
35/11. Thank you very much!!
Answer by mathemanic(13) About Me  (Show Source):
You can put this solution on YOUR website!
should x = 0.18181818...
and 100x = 18.18181818...
100x - x = 18.18181818... - 0.18181818...
99x = 18
x = 2/11
since x = 0.18181818... = 2/11, therefore
3.1818... = 3 + 0.1818...
3.1818... = 3 + 2/11
3.1818... = 35/11
Hope that helps :)