# Does .99(repeating) = 1 **URL:** \ **Category:** Factual Questions\ **Created:** [April 24, 2003, 11:03am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821 "2003-04-24T11:03:48Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Dolomite21](https://avatars.discourse-cdn.com/v4/letter/d/e5b9ba/32.png) [@Dolomite21](https://boards.straightdope.com/u/Dolomite21)\ **Post date:** [April 24, 2003, 11:03am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/1 "2003-04-24T11:03:48Z")
Given that .111(repeating) = 1/9 .222(repeating) = 2/9 .333(repeating) = 3/9 .444(repeating) = 4/9 and on and on would 9/9 equal 1 and .99(repeating)? ---
**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\ **Post date:** [April 24, 2003, 11:07am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/2 "2003-04-24T11:07:55Z")
Yes ---
**Author:** ![Dolomite21](https://avatars.discourse-cdn.com/v4/letter/d/e5b9ba/32.png) [@Dolomite21](https://boards.straightdope.com/u/Dolomite21)\ **Post date:** [April 24, 2003, 11:19am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/3 "2003-04-24T11:19:57Z")
So if infinitely speaking a number can be “rounded” up…does 2 = 4 ---
**Author:** ![phraser](https://avatars.discourse-cdn.com/v4/letter/p/a88e4f/32.png) [@phraser](https://boards.straightdope.com/u/phraser)\ **Post date:** [April 24, 2003, 11:20am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/4 "2003-04-24T11:20:11Z")
Try graphing it and you’ll have one answer. Using some math I learned in grade 12 would also give you an answer but I’ve forgotten how to do that proof :embarrassed: ---
**Author:** ![Mort\_Furd](https://avatars.discourse-cdn.com/v4/letter/m/8e8cbc/32.png) [@Mort\_Furd](https://boards.straightdope.com/u/Mort_Furd)\ **Post date:** [April 24, 2003, 11:21am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/5 "2003-04-24T11:21:13Z")
No. 9/9=1 - this is second grade mathematics, my niece is just going through this. .999 repeating does not equal 1 nor does it equal 9/9. ---
**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\ **Post date:** [April 24, 2003, 11:21am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/6 "2003-04-24T11:21:49Z")
**Dolomite21** asked: > [@](#): > > So if infinitely speaking a number can be “rounded” up…does 2 = 4 Can you provide a chain of reasoning similar to that in your first post to suggest that it might? ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [April 24, 2003, 11:23am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/7 "2003-04-24T11:23:04Z")
Let x = .99999… 10x = 9.99999… 10x - x = 9.99999… - .99999… 9x = 9 x = 1 QED ---
**Author:** ![Mort\_Furd](https://avatars.discourse-cdn.com/v4/letter/m/8e8cbc/32.png) [@Mort\_Furd](https://boards.straightdope.com/u/Mort_Furd)\ **Post date:** [April 24, 2003, 11:26am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/8 "2003-04-24T11:26:07Z")
That wasn’t nice, Lib. Shame on you for playing nasty little games like that. ---
**Author:** ![Phage](https://avatars.discourse-cdn.com/v4/letter/p/a4c791/32.png) [@Phage](https://boards.straightdope.com/u/Phage)\ **Post date:** [April 24, 2003, 11:26am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/9 "2003-04-24T11:26:28Z")
no, x = .99999… Almost the same, but not. It will be forever under 1. Infinitely small as the gap may be, it still exists. For instance, does the matter in a black hole dissappear when it is formed? ---
**Author:** ![Mort\_Furd](https://avatars.discourse-cdn.com/v4/letter/m/8e8cbc/32.png) [@Mort\_Furd](https://boards.straightdope.com/u/Mort_Furd)\ **Post date:** [April 24, 2003, 11:28am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/10 "2003-04-24T11:28:20Z")
> [@](#): > > \*Originally posted by Libertarian \*Let x = .99999… > > 10x = 9.99999… > > 10x - x = 9.99999… - .99999… > > **9x = 9** > > x = 1 Bad Lib, not supported anywhere, and not true besides. ---
**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\ **Post date:** [April 24, 2003, 11:30am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/11 "2003-04-24T11:30:03Z")
There was nothing nasty about **Libertarian’s** proof. It is perfectly valid and 0.999… does equal 1. I wish people who know nothing about mathematics would content themselves with reading these threads rather than posting in them. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [April 24, 2003, 11:31am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/12 "2003-04-24T11:31:45Z")
Give me a number between 0.999… and 1.0. (We’ve been through this before. Do a search.) ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [April 24, 2003, 11:33am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/13 "2003-04-24T11:33:17Z")
> [@](#): > > \*Originally posted by Phage \* > \*\*no, x = .99999… > > Almost the same, but not. It will be forever under 1. Infinitely small as the gap may be, it still exists. For instance, does the matter in a black hole dissappear when it is formed? \*\* There’s no gap. To invalidate the proof I gave, you have to find a flaw in the chain of deduction. Stories about black holes, however romantic and mysterious they may be, do not contradict the proof. ---
**Author:** ![GSV\_Consolation\_of\_Dreams](https://avatars.discourse-cdn.com/v4/letter/g/f1d935/32.png) [@GSV\_Consolation\_of\_Dreams](https://boards.straightdope.com/u/GSV_Consolation_of_Dreams)\ **Post date:** [April 24, 2003, 11:46am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/14 "2003-04-24T11:46:15Z")
[deadpan]Maybe someone should ask James ‘Spaceman’ Driscoll about this. He’s an authority on the subject.[/deadpan] [d&r, sniggering](http://groups.google.co.uk/groups?hl=en&lr=&ie=UTF-8&oe=UTF-8&threadm=f9ec3564.0209161551.8684e76%40posting.google.com&rnum=3&prev=/groups%3Fq%3Dspaceman%2B.999...%26ie%3DUTF-8%26oe%3DUTF-8%26hl%3Den%26btnG%3DGoogle%2BSearch) ---
**Author:** ![smiling\_bandit](https://avatars.discourse-cdn.com/v4/letter/s/e9a140/32.png) [@smiling\_bandit](https://boards.straightdope.com/u/smiling_bandit)\ **Post date:** [April 24, 2003, 11:57am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/15 "2003-04-24T11:57:46Z")
> [@](#): > > no, x = .99999… > > Almost the same, but not. It will be forever under 1. Infinitely small as the gap may be, it still exists. For instance, does the matter in a black hole dissappear when it is formed? Nope. An infintely small value does not exist, it seems. Perhaps in theory, but not in practice. ---
**Author:** ![Mort\_Furd](https://avatars.discourse-cdn.com/v4/letter/m/8e8cbc/32.png) [@Mort\_Furd](https://boards.straightdope.com/u/Mort_Furd)\ **Post date:** [April 24, 2003, 11:58am UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/16 "2003-04-24T11:58:36Z")
> [@](#): > > \*Originally posted by Jabba \* > There was nothing nasty about **Libertarian’s** proof. It is perfectly valid and 0.999… does equal 1. I wish people who know nothing about mathematics would content themselves with reading these threads rather than posting in them. Following the same “logic” will also prove that .333 repeating =1 Care to argue that one? ---
**Author:** ![Mort\_Furd](https://avatars.discourse-cdn.com/v4/letter/m/8e8cbc/32.png) [@Mort\_Furd](https://boards.straightdope.com/u/Mort_Furd)\ **Post date:** [April 24, 2003, 12:00pm UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/17 "2003-04-24T12:00:10Z")
Also, if you allow changing the base of the numbers from ten, then you can prove that everything equals one. So much for a valid proof. ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [April 24, 2003, 12:06pm UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/18 "2003-04-24T12:06:36Z")
> [@](#): > > \*Originally posted by Mort Furd \* > \*\*Following the same “logic” will also prove that .333 repeating =1 > Care to argue that one? \*\* Sure. The number between 0.333… and 1.0 is 0.666… Therefore, 0.333… does not equal 1.0. As there is no number between 0.999… and 1.0, 1.0 is equal to 0.999… ---
**Author:** ![Dolomite21](https://avatars.discourse-cdn.com/v4/letter/d/e5b9ba/32.png) [@Dolomite21](https://boards.straightdope.com/u/Dolomite21)\ **Post date:** [April 24, 2003, 12:09pm UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/19 "2003-04-24T12:09:30Z")
so using that logic…would 7 also be the middle number ---
**Author:** ![Mort\_Furd](https://avatars.discourse-cdn.com/v4/letter/m/8e8cbc/32.png) [@Mort\_Furd](https://boards.straightdope.com/u/Mort_Furd)\ **Post date:** [April 24, 2003, 12:14pm UTC](https://boards.straightdope.com/t/does-99-repeating-1/170821/20 "2003-04-24T12:14:57Z")
Following Libertarians logic: Let x = .33333… 10x = 3.33333… 10x - x = 3.33333… - .33333… 3x = 3 x = 1 QED? Something is fishy here. [Look here for a better proof.](http://mathforum.org/dr.math/faq/faq.0.9999.html) This is why I said Lib’s proof was nasty. It shows the intended result, but also shows the same result in other conditions where it doesn’t apply. [Next page](https://boards.straightdope.com/t/does-99-repeating-1/170821.md?page=2)