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Forums - General - 0.9999.... = 1.0

 

Are you convinced?

Yes 34 58.62%
 
No 20 34.48%
 
not sure 1 1.72%
 
Total:55
Player2 on 28 April 2013
Jay520 said:
 


Better picture:

For those who don't know what's going on, in a geometric series...

(only valid if r<1)

a = 9(1/10)

r = (1/10)

 

BTW, the reply to the post above is going to be hilarious.



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Jay520 on 28 April 2013
MDMAlliance said:


Oh, you were trying to say this?  That one seems to just be .9 + .09 + .009 repeating forever.  

However 9(1/10)/1-(1/10) = 1 

is not the same thing as .9 repeating.


Yeah it is. That's the formula for the sum of an infinite convergent geometric series...

a + ar + ar^2 + ar^3 + ar^4 ... repeating IS equal to a/(1-r)

That is the formula!

Now for a, input 9/10. And for r, input (1/10). This equals

9/10 + 9/10(1/10)^1 + 9/10(1/10)^2 + 9/10(1/10)^3 ....which equals .9 + .09 + .009  which equals 0.9999999

So 0.9999999 = 9/10 + 9/10(1/10) + 9/10(1/10)^2 + 9/10(1/10)^2 which equals, according to the official formula, 9/10 / [1-(1/10)]

which is 1. 



MDMAlliance on 28 April 2013
Jay520 said:
MDMAlliance said:


Oh, you were trying to say this?  That one seems to just be .9 + .09 + .009 repeating forever.  

However 9(1/10)/1-(1/10) = 1 

is not the same thing as .9 repeating.


Yeah it is. That's the formula for the sum of an infinite convergent geometric series...

a + ar + ar^2 + ar^3 + ar^4 ... repeating IS equal to a/(1-r) That is the formula.

Now for a, input 9/10. And for r, input (1/10). This equals

9/10 + 9/10(1/10)^1 + 9/10(1/10)^2 + 9/10(1/10)^3 ....which equals .9 + .09 + .009  which equals 0.9999999

So 0.9999999 = 9/10 + 9/10(1/10) + 9/10(1/10)^2 + 9/10(1/10)^2 which equals, according to the official formula, 9/10 / [1-(1/10)]

which is 1. 


No, from my class, pretty much every time with these series it meant that these series APPROACHED these numbers.  However they never actually reached them.  In calculus you simplified them to such.  The formula is simply one that is used to handle more complex geometric series, such as ones that may approach a number like .253 or something.  

However, since the sum goes on infinitely, it does not ever actually equal to the number itself.  



Jay520 on 28 April 2013
Chark said:
1 = 0.9... + ( 1 - 0.9...)

1 - 0.9... = x

1 = 0.9... + x

I don't see how this is reconcilable. The absence of an answer is not an answer.

In OP, wouldn't 9x = 8.9... not 9?


I'm not sure if you want us to answer that equation or what. But x would equal (1 - 0.9...) which is 0.0000... which is 0. meaning 1 = 0.9....

Yes, 9x can equal 8.9999... and 9. This works because 8.999..... is equal to 8 + 0.99999 which is also 8 + 1. 



NintendoPie on 28 April 2013

Yeah... all you have to do is round it up. Simple.



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Jay520 on 28 April 2013
MDMAlliance said:


No, from my class, pretty much every time with these series it meant that these series APPROACHED these numbers.  However they never actually reached them.  In calculus you simplified them to such.  The formula is simply one that is used to handle more complex geometric series, such as ones that may approach a number like .253 or something.  

However, since the sum goes on infinitely, it does not ever actually equal to the number itself.  

You can calculate the sum of an infinite series. Not what it approaches, but what it equals. Not sure what else to tell you. You just can. 

http://en.wikipedia.org/wiki/Geometric_series

Look it up anywhere else and it will tell you the same.



Chark on 28 April 2013
Jay520 said:
Chark said:
1 = 0.9... + ( 1 - 0.9...)

1 - 0.9... = x

1 = 0.9... + x

I don't see how this is reconcilable. The absence of an answer is not an answer.

In OP, wouldn't 9x = 8.9... not 9?


I'm not sure if you want us to answer that equation or what. But x would equal (1 - 0.9...) which is 0.0000... which is 0. meaning 1 = 0.9....

Yes, 9x can equal 8.9999... and 9. This works because 8.999..... is equal to 8 + 0.99999 which is also 8 + 1. 


Wouldn't it actually have to be repeating y and not repeating zero? I would consider it repeating zero but the actual quantity trying to be subtracted from one is not definitive.



Before the PS3 everyone was nice to me :(

Jay520 on 28 April 2013
Chark said:
Jay520 said:
Chark said:
1 = 0.9... + ( 1 - 0.9...)

1 - 0.9... = x

1 = 0.9... + x

I don't see how this is reconcilable. The absence of an answer is not an answer.

In OP, wouldn't 9x = 8.9... not 9?


I'm not sure if you want us to answer that equation or what. But x would equal (1 - 0.9...) which is 0.0000... which is 0. meaning 1 = 0.9....

Yes, 9x can equal 8.9999... and 9. This works because 8.999..... is equal to 8 + 0.99999 which is also 8 + 1. 


Wouldn't it actually have to be repeating y and not repeating zero? I would consider it repeating zero but the actual quantity trying to be subtracted from one is not definitive.


repeating y? What is y?



trollmaster85 on 28 April 2013

So, 1 / 0.0..01 = (9)
Therefore 1/0 = infinity => 0 * infinity = 1 => 0 = 1;



Soleron on 28 April 2013
MDMAlliance said:
Soleron said:
Jay520 said:
...


Better picture:

This explanation, and the realisation that a single number can have more than one representation in decimal numbers (example: 0.35, 0.350, 0.3500, 0.35000... are all the same number) should be enough for anyone numerate. There is no dispute, it's the same quantity as 1 represents.


I take it math isn't your strong subject?  That or you haven't taken higher levels of math.  The whole distinction for 0.35 and 0.350 and going on is mostly a distinction made for science.  They use it to keep their "significant figures" as they need to keep their measurements as accurate as they were able to measure, whatever they were measuring, with.

Top-10 university Physics degree with considerable maths content. It's just an example to show that two different decimal numbers equal the same number, which is usually the hurdle for not understanding this problem.

You can try to make "proofs" that .9 repeating = 1, but this only can work if you ignore the fact that our decimal system doesn't work perfectly.

They're not proofs that .9999=1, they're examples that show they both represent the same number.

Nothing in this thread so far is a rigorous proof, but that doesn't change the conclusion.