Question 497688
1/3 times 3 is equal to both so using equations,

1/3(3)=1/3(3)

.9 repeated =1/3(3)
1= 1/3(3)

.9 repeated = 1

The infinite series equation for this...
so .9 is 9/10 
.99 is 99/100
.999 is 999/1000
.9999 is .9999/10000
You can see where is am going with this... 
if not keep scrolling.. 
.9 + .09 + .009 + .0009 = .9999
.09 = 9/100
.009 = 9/1000
.0009 = 9/10000
so you are essentially adding 
9/10 + 9/100 + 9/1000 +9/10000 
So the geometric series version is...

sum ( 9/(10)^n , n, 1, forever)  and..... = 1