# Prove that 0.999999999(9)=1

### Prove that 0.999999999(9)=1

Prove that
0.999999999(9)=1
Math Tutor

Posts: 396
Joined: Sun Oct 09, 2005 11:37 am
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### Re: Prove that 0.999999999(9)=1

$0.999999999(9) = 0.(9)=0.9+0.09+0.009+......=0.9+0.9*10+0.9*10^{2}+......$ Right?
So $0.(9)$- Indefinitely - decreasing geometric fraction
But we know formula for Indefinitely - decreasing geometric fraction,$S=\frac{b_1}{1-q }$ , where q = 0.1
$S=\frac{0.9}{1-0.1 } = \frac{0.9}{0.9 } = 1.$
Guest

### Re: Prove that 0.999999999(9)=1

Interesting solution but I think that this should be proved using limes.
Guest

### Re: Prove that 0.999999999(9)=1

Formula for Indefinitely - decreasing geometric fraction is proven by limes!!!

shemet

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Joined: Tue Jun 14, 2011 7:59 am
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### Re: Prove that 0.999999999(9)=1

We will prove that 0,(9)=1
0,(9)=0,9(9)=x
So 10x=x+9 so x=1
Guest

### Re: Prove that 0.999999999(9)=1

Hey guest that was interesting solution but this can be also solved through limit and will be more easy by using scientific notation calculator it can be done in a second.
Guest

### Re: Prove that 0.999999999(9)=1

I am not sure and it has not to be calculated and proved.

Math Tutor

Posts: 396
Joined: Sun Oct 09, 2005 11:37 am
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### Re: Prove that 0.999999999(9)=1

Sorry, I have also no idea about it.

Alicelewis11

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Location: USA
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### Re: Prove that 0.999999999(9)=1

I don't think that there is any real prove of this problem. It is just assumed equal to 1 or we can say that to round off the fraction digit we write 0.999999 equal to 1.

leesajohnson

Posts: 208
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Location: London
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### Re: Prove that 0.999999999(9)=1

It is already proved(the second post) using geometric progression.
Guest

### Re: Prove that 0.999999999(9)=1

It is already proved(the second post) using geometric progression......Query......

Are you sure about the second post......is it not just saying it converges on 1 because it is converging.......but never gets there...??????
Guest

### Re: Prove that 0.999999999(9)=1

If one item has a value of 0.99999999999999......
Then 10 items have a total value of 9.9999999999999999.......
Subtract the one item from ten items gives nine items have total value of 9.000000000000..... or just 9.0
Divide value of nine items by nine to get value of one item, this gives value of 1.0 as the value of one item.

So original given value of one item as 0.99999999999......is same as calculated value of one item equals 1.0000000000 OR just 1.
Guest

### Re: Prove that 0.999999999(9)=1

Subtract the one item from ten items gives nine items have total value of 9.000000000000..... or just 9.0

Sorry...I meant to say last post..........

Subtract the value of one item (0.999999999....) from the value of ten items gives the total value of nine items as 9.000000000000..... or just 9.0

....................................
Guest