I first started thinking about this when I was using a formula to find out the fraction for .9 repeating and I got 1. here's the formula:

 

 

 

 let n= repeating decimal

   n        =     .9

 -10n          -9.9

-----------------------

-9n              -9



-9/-9          -9/-9

 1n               = 1 ?!?!

 

 

 

This formula works for every repeating decimal except .9 repeating. (if your repeating number is more than 1 digit add one 0 to 10 for every extra digit)

 

 

 

More proof:

 

In decimal form, 

1/3 + 2/3 = .9 repeating



1/7 + 6/7 = .9 repeating

2/7 + 5/7 = .9 repeating

3/7 + 4/7 = .9 repeating



1/9 + 8/9 = .9 repeating

2/9 + 7/9 = .9 repeating

3/9 + 6/9 = .9 repeating

4/9 + 5/9 = .9 repeating



1/11 + 10/11 = .9 repeating

2/11 + 9/11 = .9 repeating

3/11 + 7/11 = .9 repeating

4/11 + 5/11 = .9 repeating

5/11 + 6/11 = .9 repeating

 

 

 

 

 

What do you think?

 

 

 

Can .9 repeating really equal one?!

 

 

 

 

 

If you have more proof please post and I will add.

 

 

 

 

 

Edit #1: I added on to the fraction list.

 

Edit #2: I put fraction list in code.

More proof:

 

In decimal form,

 

1/3 + 2/3 = .9 repeating

 

2/7 + 5/7 = .9 repeating

 

1/11 + 10/11 = .9 repeating

 

 

 

 

 

very interesting.. got me thinking.. A+

Thanks LP = )

 

 

 

Anyone find more fractions or anything?

 

 

 

off to dinner. Will be back in 20 minutes.

I use the thirds for that

 

 

 

1/3=.3 repeating

 

multiply through by 3

 

3*(1/3=.33...)

 

3/3=.9 repeating

 

1=.9 repeating

 

it's simpler than yours O.o

double post :?

But 3/3 is equal to one.

 

So you cant use that fraction to equal .9 repeating.

 

But if that were true you would be able to use 7/7, 9/9, and 11/11 for it to.

 

 

 

 

 

but 1/3 + 2/3 in decimals is equals . 9 repeating.

1/3 in decimals times 3 equals .9 repeating

 

1/3 in fractions times 3 equals 1

 

 

 

and if 1/3=.3 repeating then yes it does work

So you think the number .9 repeating doesn't exist?

GAH?! :shock:

GAH?! :shock:

 

 

 

Exactly.

 

 

 

Mind if I siggy that?

So you think the number .9 repeating doesn't exist?

 

 

 

Well it does exist, but you can't really use it for anything since it's equal to one, I don't know if that makes it imaginary or what

 

it can't be written as a fraction so I would assume that yes, it's an imaginary number

Numbers that can't be put into fractions are irrational, not imaginary. Such as, the square root of 2.

:shock: ? why are you all making topics that make us think, its the summer!

0.3 recurring is just the nearest decimal representation of 1/3. 0.3 recurring * 3, if done correctly, would not equal 0.9 recurring, it would equal 1. 0.9 recurring is a result of lack of precision; precision which is impossible to exercise.

Never thought of that before.

 

I'll join Biabf. GAH?!

I don't understand a [cabbage] from that! =P~

I'm spreading my misery on you during summer because I had to take a class so I could get bumped from regular math to honors algebra during the summer, final test is tommorow.

 

 

 

Off topic: Some times I see all the emotes and then I see the "CLick to view more motes" :?

 

 

 

Off topic once more: Weird, off topic in an off topic forum.

Basically .9 repeating gets infinitely close to 1, and basically yeah, that equals 1. Just like 1 divided by infinity equals zero. You're finding the limit of the repeating decimal.

Never thought of that before.

 

I'll join Biabf. GAH?!

 

 

 

I'll join both of you.. GAH?! I mean it's summer... I'm not supposed to think =;

As the decimal .9999999... gets longer, the difference between it and one becomes so infinitesimally small it's insignificant and basicly 0.

this is one of many reasons i hate math.

 

 

 

it in the end.. there is no solution.. just a bunch of numbers..

 

 

 

i beleive Beavis and Butthead once said..

 

 

 

"numbers suck"

 

 

 

and i totally agree... =D>

I'm spreading my misery on you during summer because I had to take a class so I could get bumped from regular math to honors algebra during the summer, final test is tommorow.

 

 

 

Off topic: Some times I see all the emotes and then I see the "CLick to view more motes" :?

 

 

 

Off topic once more: Weird, off topic in an off topic forum.

 

 

 

Speaking of that....

 

 

 

/me goes to check on his Trig class >.<

Very interesting. good job. =D>. But fractions and decimals are very different ways of looking at math maybe they arn't as interchangable as we thought :-k .

As others have said, its a matter of precision. The calculator can't get the exact value for 1/3, so it approximates. That's why you have .99® as the answer. Whenever you see that, just read it as 1.

0.999... = 1

 

Its one of those things that goes against the intuition of a lot of people but if youÃÆââââ¬Å¡Ã¬Ã¢ââ¬Å¾Ã¢ve done basic high school maths then you should know about limits and know that things can limit to whole numbers. I just see 0.999.. as a geometric series and the limit of that series is 1.

 

 

 

http://en.wikipedia.org/wiki/Proof_that_0.999..._equals_1

 

Has a bunch of proofs. For the unbelievers, tough :boohoo:

 

 

 

Edit: and how did I know this was going to be a 0.999...=1 topic from the title.