SOLUTION: using the infinite series equation, explain how .9 repeating equals one. I tried to do it by myself, but I cannot figure it out. Please help me, but not give me a direct answer.

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Question 497688: using the infinite series equation, explain how .9 repeating equals one. I tried to do it by myself, but I cannot figure it out. Please help me, but not give me a direct answer.
Found 2 solutions by MrMitchell, Evy Hofbauer:
Answer by MrMitchell(3) (Show Source):
You can put this solution on YOUR website!
The correct answer is:
.9 repeating actually ever equals one. It's just simply so close, that 1 is theoretically equal.

Answer by Evy Hofbauer(7) (Show Source):
You can put this solution on YOUR website!
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