Prove that 0.999999999(9)=1

Prove that 0.999999999(9)=1

Postby Math Tutor » Wed Jul 27, 2011 4:20 am

Prove that
0.999999999(9)=1

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Re: Prove that 0.999999999(9)=1

Postby Guest » Wed Aug 03, 2011 8:57 am

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

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Re: Prove that 0.999999999(9)=1

Postby Guest » Wed Aug 03, 2011 1:08 pm

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

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Re: Prove that 0.999999999(9)=1

Postby shemet » Sat Aug 06, 2011 1:31 pm

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

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Re: Prove that 0.999999999(9)=1

Postby Guest » Sun Aug 07, 2011 12:55 pm

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

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Re: Prove that 0.999999999(9)=1

Postby Guest » Sat Feb 04, 2012 3:47 am

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.

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Re: Prove that 0.999999999(9)=1

Postby Math Tutor » Sat Feb 04, 2012 7:52 am

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

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Re: Prove that 0.999999999(9)=1

Postby Alicelewis11 » Tue Jul 22, 2014 11:55 am

Sorry, I have also no idea about it. :cry: :cry:

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Re: Prove that 0.999999999(9)=1

Postby leesajohnson » Thu Mar 31, 2016 5:12 am

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.

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Re: Prove that 0.999999999(9)=1

Postby Guest » Thu Mar 31, 2016 6:32 am

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

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Re: Prove that 0.999999999(9)=1

Postby Guest » Thu Mar 31, 2016 6:50 am

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...??????

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Re: Prove that 0.999999999(9)=1

Postby Guest » Thu Mar 31, 2016 7:05 am

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.

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Re: Prove that 0.999999999(9)=1

Postby Guest » Thu Mar 31, 2016 7:14 am

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

....................................

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