Question

how to change this recurring decimal into fractions. 0.9'

Answer 1

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

Answer 2

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= ??

Answer 3

.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