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.9 repeating equals 1
http://www.yarrthepirate.com/phpbb3/viewtopic.php?f=5&t=6342		 Page 1 of 4
Author:  Led [ Thu Aug 25, 2005 3:36 pm ]
Post subject:  .9 repeating equals 1
Interesting thing my math teacher brought up today and i figured id make a thread about it.

1/3 = .333...

and

2/3 = 0.666....

and

1/3 + 2/3 = 1

So what do you guys think. Personally i really am not sure what to believe lol. Also there are more proofs for this, this is just the simplest one.
Author:  Feep [ Thu Aug 25, 2005 4:27 pm ]
Post subject: 
What you offered is not a "proof", so to speak, simply an observation...this is generally more of a "philosophical" question than a mathematical one, since the difference between the two numbers is infinitely small. I'm trying to think of a situation in calculus where a differentiation of the two would apply, but I can't...I severely doubt there are any circumstances where they aren't really treated the same. Yeah, they're equal.
Author:  Matti [ Thu Aug 25, 2005 4:35 pm ]
Post subject: 
Yes

.9999999... = .9 + .09 + .009 + .0009 ...

so we can have a series:

(9/10) * sum( from n = 0 to infinity, .1^n)



a/(1 - r)

where a = 9/10
and r = .1

so we have

(.9)/(.9) = 1



EDIT: That might be hard for some to read. Let me explain a little. 0.999999 repeating can be represented by an infinite geometric series.

0.9 + 0.09 + 0.009 + ... and so on. Using the formula, (t1)/(1-r) where t1 is the first term and r is the rate, plug in the numbers. You get:

0.9/1-0.1 = 0.9/0.9 = 1.
Author:  Ponuh [ Thu Aug 25, 2005 4:38 pm ]
Post subject: 
God I hate math
Author:  Pirato [ Thu Aug 25, 2005 4:46 pm ]
Post subject: 
I don't care, I hate maths.
Author:  Matti [ Thu Aug 25, 2005 4:48 pm ]
Post subject:  Re: .9 repeating equals 1
Ledzeppelin wrote:
Interesting thing my math teacher brought up today and i figured id make a thread about it.

1/3 = .333...

and

2/3 = 0.666....

and

1/3 + 2/3 = 1

So what do you guys think. Personally i really am not sure what to believe lol. Also there are more proofs for this, this is just the simplest one.


After reading this again I see what your teacher is getting at.

1/3 = .333...

.333... + .333... + .333... = .999...

Because 1/3 = .333... That means that 1/3 + 1/3 + 1/3 = 3/3 = 1


Math is fun omg :dbanana:
Author:  Ponuh [ Thu Aug 25, 2005 4:52 pm ]
Post subject: 
I want to hear ike's explanation of this.
Author:  Reinheld [ Thu Aug 25, 2005 5:26 pm ]
Post subject: 
Nerd alert.
Author:  Yarr [ Thu Aug 25, 2005 5:35 pm ]
Post subject: 
someone go give mattie a wedgie
Author:  Parade [ Thu Aug 25, 2005 5:36 pm ]
Post subject: 
ponuh wrote:
I want to hear ike's explanation of this.


haha im horrible at math, and i dont have an explination. but i do know that this is/isnt true, if your gonna be a real bitch about it, then its not, because in reality, it will never equal 1.

but even a calculator will round it off to 1 because after so many 9's it because to rediculasly confusing and retarted that it will be so close to 1 that it doesnt even make a single bit of difference.

EDIT: nvm, i dont even wana say what i think it is, because i could care less,
Author:  Mikey [ Thu Aug 25, 2005 5:36 pm ]
Post subject: 
isn't it missing .1 for it to equal a compete full whole number 1?
Author:  Yarr [ Thu Aug 25, 2005 5:37 pm ]
Post subject: 
Mikey wrote:
isn't it missing .1 for it to equal a compete full whole number 1?


lol mikey.

I know youre not trying to be funny
Author:  Mikey [ Thu Aug 25, 2005 5:39 pm ]
Post subject: 
i'm actually confused lol. And btw i'm horrible at math. IRL i use my fingers. I constantly look like a fool lol
Author:  Yarr [ Thu Aug 25, 2005 5:40 pm ]
Post subject: 
Mikey wrote:
i'm actually confused lol. And btw i'm horrible at math. IRL i use my fingers. I constantly look like a fool lol



You? Bad at math?

IMPOSSIBLE!
Author:  Mikey [ Thu Aug 25, 2005 5:44 pm ]
Post subject: 
Yarr wrote:
Mikey wrote:
i'm actually confused lol. And btw i'm horrible at math. IRL i use my fingers. I constantly look like a fool lol



You? Bad at math?

IMPOSSIBLE!


you actually thinking you're funny !!

IMPOSSIBLE!! lol
Author:  Pirato [ Thu Aug 25, 2005 5:49 pm ]
Post subject: 
All I know is it's not 1. If it would be 1 it would be 1. This is 0.99999... As hard as it's trying to be 1, it's never going to be that. That is because it is infinitely smaller than 1.
Author:  Matti [ Thu Aug 25, 2005 6:02 pm ]
Post subject: 
Pirato wrote:
All I know is it's not 1. If it would be 1 it would be 1. This is 0.99999... As hard as it's trying to be 1, it's never going to be that. That is because it is infinitely smaller than 1.


Not true.

A number is a number and can't equal another number, right? That is the mindset that keeps people from accepting this equation. Well .999... is NOT a number; it's a series which is how it works out.
Author:  Mikey [ Thu Aug 25, 2005 6:04 pm ]
Post subject: 
you are saying that .999 isn't a number so how does it equal 1 if isn't a number in the first place? I are confused please explain
Author:  Matti [ Thu Aug 25, 2005 6:05 pm ]
Post subject: 
Mikey wrote:
you are saying that .999 isn't a number so how does it equal 1 if isn't a number in the first place? I are confused please explain


Read this and think about it:

Quote:
That might be hard for some to read. Let me explain a little. 0.999999 repeating can be represented by an infinite geometric series.

0.9 + 0.09 + 0.009 + ... and so on. Using the formula, (t1)/(1-r) where t1 is the first term and r is the rate, plug in the numbers. You get:

0.9/1-0.1 = 0.9/0.9 = 1.
Author:  Parade [ Thu Aug 25, 2005 6:11 pm ]
Post subject: 
ok. .9 +.1 = 1 correct?... well you can have an infanite number of nines... .99999999999999999999999999999999999999999999999999999999999999999999999999999999999999.... and 1.0 is still geater by an infinate ammount. the decimal places can go on forever. now a caulucator that reads .9999999999999999999999999999999999999999999999999999999
99999999(alot more 99999999999...)

will eventualy just round itself off to a whole number. (1.0) but thats only because it gets to soo many digits that its just not worth keeping track off.

here is an example my math teacher gave us about a week ago..

lets say i was 10 inches from a wall, and i went half of that closer to the wall, so now im at 5 inches, and i went half way closer, now im at 2.5 inches... if i kept going half waly closer than the number before, i will NEVER reach the wall. i will get so close that i am virtualy tehre, but i will never bee touching the wall.

same thing with .9 repeating. its so close that its virtualy 1.0, but irl its not.
Author:  Ponuh [ Thu Aug 25, 2005 6:45 pm ]
Post subject: 
number cannot equal number unless it's the same number.

Led's little thing though is just a small breakdown in the fact that we round everything so often or something I think.
Author:  Mikey [ Thu Aug 25, 2005 6:52 pm ]
Post subject: 
Matti wrote:
Mikey wrote:
you are saying that .999 isn't a number so how does it equal 1 if isn't a number in the first place? I are confused please explain


Read this and think about it:

Quote:
That might be hard for some to read. Let me explain a little. 0.999999 repeating can be represented by an infinite geometric series.

0.9 + 0.09 + 0.009 + ... and so on. Using the formula, (t1)/(1-r) where t1 is the first term and r is the rate, plug in the numbers. You get:

0.9/1-0.1 = 0.9/0.9 = 1.


here's an answer to the equation from mikey himself

Go fuck yourself
Author:  Matti [ Thu Aug 25, 2005 6:52 pm ]
Post subject: 
/sigh

You guys need to take some upper level math. This is as common a question as the thing about the hotel room for $30.00.
Author:  Mikey [ Thu Aug 25, 2005 6:53 pm ]
Post subject: 
i was kidding wench
Author:  Vurin [ Thu Aug 25, 2005 7:36 pm ]
Post subject: 
Hotel Room for $30? never heard that one...

My math knowledge stops at jokes like about ntus and saying "gee, I'm a tree"
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