Math: .9 repeating equals 1

Discussion in 'Community Discussion' started by Fearless Leader, Aug 23, 2007.

  1. Fearless Leader macrumors 68020

    Mar 21, 2006
    I got bored after a math test and was just messing around and realized something that makes sense and doesn't make sense at the same time.

    1/3 = .3 repeating
    2/3 = .6 repeating
    following the trend
    3/3 = .9 repeating
    3/3 = 1/1 which is 1.

    Where Did I go wrong? or did I?

    also: psst Q Add a math section. It'll be great. You know you want one.
  2. Fearless Leader thread starter macrumors 68020

    Mar 21, 2006
    ohh thanks thats cool. I didn't even think of googleing/wiking this.

    Its strange, I proved it (if only I did this a couple hundred years ago, I could have been remembered or something) but it doesn't seem right, but it is.
  3. steamboat26 macrumors 65816


    May 25, 2006
    Arlington VA
    I had never thought about that before...

    Thats a long Wikipedia entry for one number! :eek:
  4. ChrisBrightwell macrumors 68020


    Apr 5, 2004
    Huntsville, AL
    Basically, the "lightbulb" moment for me was when I realized that an infinitessimal value, on the real number system, is equal to zero.

    That is:

    0.000...[infinitely many zeroes]...0001 is, on the real number line, equal to zero.

    So ...
    1/3 = 0.333...

    1/3 * 3
    = 0.333... * 3
    = 0.999...
    = 1 - 0.000...001
    = 1 - 0
    = 1

    I feel like I grossly over-simplified it, but I hope that makes sense.
  5. Rodimus Prime macrumors G4

    Rodimus Prime

    Oct 9, 2006
    ah I used to think about stuff like this. Then I got into college and engineering work. That when I learned anything past 3-4 decimal is pretty worthless any how. That includes when I am using scientific notation. I will only go 3-4 points past the decimal in my work and my answer will be 2-3 past.
    Reason I know it is worthless is it effects the answer so little that it does not matter. My though is I am with in one hundredth of the correct answer so it is close enough.
  6. jdechko macrumors 68040

    Jul 1, 2004
    And a more local discussion used to be here. ;) Boy that one was fun.

    Also, I prefer my explanation from said thread that if someone offered to give me a $1,000,000 and I really only got $999,999.99, I wouldn't be to upset. :D
  7. bemylover macrumors regular

    Jun 20, 2005
    yep, 0.999999... is exactly 1. If it was not exactly 1 then there would be some other number that would be greater than 0.99999... and less then 1 and as there is no such number these two are the same.

    Nice observation :)
  8. Jasonbot macrumors 68020


    Aug 15, 2006
    The Rainbow Nation RSA
    There was this funny simplification of fractions thing I did in maths a few years ago that showed how .999... is equal to 1. I can't remember it though.
  9. johnee macrumors 6502a


    I'm not buying it.

    9 is a pretty evil number. it's always been jealous of 1, and it's been trying to make itself known for a long time now.

    For instance, this little trick:
    1 x 9 = 9
    2 x 9 = 18 (1+8=9)
    3 x 9 = 27 (2+7=9)
    457 x 9 = 4113 (4+1+1+3=9)

  10. swiftaw macrumors 603


    Jan 31, 2005
    Omaha, NE, USA
    Probably something like this

    x = 0.99999....

    so 10x = 9.99999........

    so 10x - x = 9.99999..... - 0.99999.... = 9

    so 9x = 9

    so x = 9/9 = 1

    Actually this method works to convert any reoccurring decimal into a fraction, for example
    x = 0.838383.......
    100x = 83.838383.....
    99x = 83
    x = 83/99
  11. Jasonbot macrumors 68020


    Aug 15, 2006
    The Rainbow Nation RSA
    Aaah! The memories :D Thanks!
    luckily in grade 11 my casio FX 82-ES does fractions for me these days.
  12. gertruded macrumors regular

    Jul 5, 2007
    Northwestern Illinois
    In the days when we used slide rules to do all our calculations, we were limited to 3 significant places. In that practical context .999 definitely is not equal to 1.00. I still laugh when I see calculations done computers displayed to 5 or more significant figures for ordinary engineering calculations.

    The slide rule was an extraordinary device. Mine was a Post log log duplex versilog, made of bamboo. I still have it and it still works without electricity.

  13. tominated macrumors 68000


    Jul 7, 2006
    Queensland, Australia
    wow. i think i just had a mini stroke.

    well, not really
  14. Fearless Leader thread starter macrumors 68020

    Mar 21, 2006
    ohh I really like that one. I went over it with my Math teacher today. He went from not believing me, to helping me to get him to agree, then agreeing.

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