how to change this recurring decimal into fractions. 0.9'

Question

how to change this recurring decimal into fractions.  0.9'

unklerhaukus · Answer

let     x = 0.9'
     10x = 9.9'
       9x = 
         x =

phi · Answer

in other words,  if x= 0.9999.....
and 10x= 9.9999.....
what do you get if you subtract x from 10x
 10x=    9.9999.... 
-   x= - 0.99999....
___________________
    9x= ??

anonymous · Answer

.9 recurring as a fraction is 9/9 = 1
 
Any pure recurring decimal is just that number divided by 9, for example:
 
.1 recurring is 1/9
 
.4 recurring is 4/9
 
In the case of .9 recurring it turns out that it's 1. There is a mathematical proof for this, but I don't have that remembered off the top of my head. Good Luck