# Math: .99repeating = 1? **URL:** \ **Category:** Factual Questions\ **Created:** [April 12, 2000, 1:59pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021 "2000-04-12T13:59:00Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Flat\_U.Lance](https://avatars.discourse-cdn.com/v4/letter/f/90db22/32.png) [@Flat\_U.Lance](https://boards.straightdope.com/u/Flat_U.Lance)\ **Post date:** [April 12, 2000, 1:59pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/1 "2000-04-12T13:59:00Z")
Is the repeating decimal .9999999 equal to 1? .33333 repeating is equal to one third. .6666 repeating is equal to two thirds. .333333 + .66666 = 1 Some math nerds like bigneck say that .9999 repeating is not equal to 1. * * * Don’t listen to bigneck. ---
**Author:** ![bigneck](https://avatars.discourse-cdn.com/v4/letter/b/6f9a4e/32.png) [@bigneck](https://boards.straightdope.com/u/bigneck)\ **Post date:** [April 12, 2000, 2:26pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/2 "2000-04-12T14:26:00Z")
Flat, .87632 = .87632 17 = 17 1 = 1 .99999999 = .99999999 you = dork bigneck ---
**Author:** ![AWB](https://avatars.discourse-cdn.com/v4/letter/a/bb73d2/32.png) [@AWB](https://boards.straightdope.com/u/AWB)\ **Post date:** [April 12, 2000, 2:27pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/3 "2000-04-12T14:27:00Z")
Yes, it’s the same. E.g., \\code:\\\ Fractions: 2/7 + 5/7 = 7/7 = 1 Decimals: * * * 0.285714 + 0.714285 = 0.999999 Fractions: 2/9 + 7/9 = 9/9 = 1 Decimals: * * * 0.2 + 0.7 = 0.9 ```auto ------------------ Wrong thinking is punished, right thinking is just as swiftly rewarded. You'll find it an effective combination. ``` ---
**Author:** ![AWB](https://avatars.discourse-cdn.com/v4/letter/a/bb73d2/32.png) [@AWB](https://boards.straightdope.com/u/AWB)\ **Post date:** [April 12, 2000, 2:28pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/4 "2000-04-12T14:28:00Z")
\*\*AAUUGGHH! I fed the trolls! Now they’ll proliferate! * * * Wrong thinking is punished, right thinking is just as swiftly rewarded. You’ll find it an effective combination. ---
**Author:** ![bigneck](https://avatars.discourse-cdn.com/v4/letter/b/6f9a4e/32.png) [@bigneck](https://boards.straightdope.com/u/bigneck)\ **Post date:** [April 12, 2000, 2:29pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/5 "2000-04-12T14:29:00Z")
Flat, .87632 = .87632 17 = 17 1 = 1 .99999999 = .99999999 you = dork bigneck ---
**Author:** ![bigneck](https://avatars.discourse-cdn.com/v4/letter/b/6f9a4e/32.png) [@bigneck](https://boards.straightdope.com/u/bigneck)\ **Post date:** [April 12, 2000, 2:31pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/6 "2000-04-12T14:31:00Z")
Sorry for posting that last one twice - if I did. Actually, .333333 + .66666 = .999993 ---
**Author:** ![handy](https://avatars.discourse-cdn.com/v4/letter/h/b5a626/32.png) [@handy](https://boards.straightdope.com/u/handy)\ **Post date:** [April 12, 2000, 2:38pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/7 "2000-04-12T14:38:00Z")
We already answered this one down below. What is it with the logic people anyway? 1 does not & is not a 9 period. ---
**Author:** ![Flat\_U.Lance](https://avatars.discourse-cdn.com/v4/letter/f/90db22/32.png) [@Flat\_U.Lance](https://boards.straightdope.com/u/Flat_U.Lance)\ **Post date:** [April 12, 2000, 2:41pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/8 "2000-04-12T14:41:00Z")
Hey Handy, where was this answered before? ---
**Author:** ![RussellM](https://avatars.discourse-cdn.com/v4/letter/r/ed8c4c/32.png) [@RussellM](https://boards.straightdope.com/u/RussellM)\ **Post date:** [April 12, 2000, 2:47pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/9 "2000-04-12T14:47:00Z")
zero point…repeating Russell ---
**Author:** ![RussellM](https://avatars.discourse-cdn.com/v4/letter/r/ed8c4c/32.png) [@RussellM](https://boards.straightdope.com/u/RussellM)\ **Post date:** [April 12, 2000, 2:55pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/10 "2000-04-12T14:55:00Z")
Last discussed [Is 0.999…=1 ?](http://boards.straightdope.com/ubb/Forum3/HTML/007229.html) The last entry in this thread was only 5 days ago. Russell ---
**Author:** ![C\_K\_Dexter\_Haven](https://avatars.discourse-cdn.com/v4/letter/c/b2d939/32.png) [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)\ **Post date:** [April 12, 2000, 3:00pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/11 "2000-04-12T15:00:00Z")
Another way to approach this, is that .99999… = SUM (9\*10^-n) as n --\> infinity. It can easily be shown that this infinite sum is 1. ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [April 12, 2000, 4:04pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/12 "2000-04-12T16:04:00Z")
CKDExtHavn, you sound like Fermat in your last post. ---
**Author:** ![Jinx](https://avatars.discourse-cdn.com/v4/letter/j/c6cbf5/32.png) [@Jinx](https://boards.straightdope.com/u/Jinx)\ **Post date:** [April 13, 2000, 5:15am UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/13 "2000-04-13T05:15:00Z")
THINK! For goodness sake! Ask yourself if 0.333 = 0.3333? Is 0.3333 repeating = 0.333? What is 1/3? Without saying “repeating”, there would be NO exact decimal equivalent! You see that, from this example, 0.9999 repeating ad infinitum is still \< 1! These are two distinct numbers! * * * “They’re coming to take me away ha-ha, ho-ho, hee-hee, to the funny farm where life is beautiful all the time… :)” - Napoleon IV ---
**Author:** ![emarkp](https://avatars.discourse-cdn.com/v4/letter/e/3be4f8/32.png) [@emarkp](https://boards.straightdope.com/u/emarkp)\ **Post date:** [April 13, 2000, 5:49am UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/14 "2000-04-13T05:49:00Z")
Sigh. [Is 0.999…=1 ?](http://boards.straightdope.com/ubb/Forum3/HTML/007229.html) Yes, they’re equal. Go see the other thread. ---
**Author:** ![C\_K\_Dexter\_Haven](https://avatars.discourse-cdn.com/v4/letter/c/b2d939/32.png) [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)\ **Post date:** [April 12, 2000, 6:53pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/15 "2000-04-12T18:53:00Z")
Hey, Jinx! Think!! 1 = 1. 4 = 4. .25 = .25 Therefore, 1/4 can’t equal .25, can it? Sheeeeeeesh. [/sarcasm] .333 is not equal to 1/3 .333333333333 is not equal to 1/3 .33333333[1 billion 3’s]33 is not equal to 1/3 but .3333… where the decimal 3 repeats infinitely many times IS in fact, equal to 1/3. ---
**Author:** ![CheapBastid](https://avatars.discourse-cdn.com/v4/letter/c/8baadc/32.png) [@CheapBastid](https://boards.straightdope.com/u/CheapBastid)\ **Post date:** [April 12, 2000, 9:14pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/16 "2000-04-12T21:14:00Z")
_Again_ with the [Infinities](http://www.greylabyrinth.com/Puzzles/puzzle006.htm)… ---
**Author:** ![tony1234](https://avatars.discourse-cdn.com/v4/letter/t/4491bb/32.png) [@tony1234](https://boards.straightdope.com/u/tony1234)\ **Post date:** [April 12, 2000, 10:20pm UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/17 "2000-04-12T22:20:00Z")
Again, I suggest we be a little more charitable. Many people have the understandable intuition that .9 repeating does not equal 1. This intution can be modelled in nonstandard number systems without contradition (or so I have heard). The existence of infintesimals is no more problematic than the existence of imaginary numbers. Tony * * * Two things fill my mind with ever-increasing wonder and awe: the starry skies above me and the moral law within me. – Kant ---
**Author:** ![pipefitter](https://avatars.discourse-cdn.com/v4/letter/p/97f17d/32.png) [@pipefitter](https://boards.straightdope.com/u/pipefitter)\ **Post date:** [April 13, 2000, 12:24am UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/18 "2000-04-13T00:24:00Z")
Now ask a machinist if .9999 is equal to one. Most likely he will say no, because they are used to working in tollerences where that .0001 might make a difference in the way a part fits * * * Hand me that wrench. No, the one that looks like a hammer. Sig Courtesy of Walley ---
**Author:** ![Monty](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/monty/32/47_2.png) [@Monty](https://boards.straightdope.com/u/Monty)\ **Post date:** [April 13, 2000, 3:03am UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/19 "2000-04-13T03:03:00Z")
But, you see, pipefitter, not only are we not talking about machinists and fittings, we’re also not talking about .9999. We’re discussing 0.99999… (“Zero point Nine (with the 9 repeating ad infinitum)”). Thus, I think I’ll go with the answer posted by the professional mathematician above who’s already stated for us that not only does 0.99999… (“Zero point Nine (with the 9 repeating ad infinitum)”) equal 1, but that it’s easily proved. ---
**Author:** ![Red\_2](https://avatars.discourse-cdn.com/v4/letter/r/a5b964/32.png) [@Red\_2](https://boards.straightdope.com/u/Red_2)\ **Post date:** [April 13, 2000, 3:17am UTC](https://boards.straightdope.com/t/math-99repeating-1/11021/20 "2000-04-13T03:17:00Z")
test * * * “I’m hungry, let’s get a taco.” - Mr. White [Next page](https://boards.straightdope.com/t/math-99repeating-1/11021.md?page=2)