Math: .9 repeating equals 1

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

  1. Fearless Leader macrumors 68020

    Joined:
    Mar 21, 2006
    Location:
    Hoosiertown
    #1
    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
    but
    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

    Joined:
    Mar 21, 2006
    Location:
    Hoosiertown
    #3
    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

    steamboat26

    Joined:
    May 25, 2006
    Location:
    Arlington VA
    #4
    I had never thought about that before...

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

    ChrisBrightwell

    Joined:
    Apr 5, 2004
    Location:
    Huntsville, AL
    #5
    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

    Joined:
    Oct 9, 2006
    #6
    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

    Joined:
    Jul 1, 2004
    #7
    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

    Joined:
    Jun 20, 2005
    #8
    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

    Jasonbot

    Joined:
    Aug 15, 2006
    Location:
    The Rainbow Nation RSA
    #9
    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

    johnee

    #10
    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)

    EVIL!!!!
     
  10. swiftaw macrumors 603

    swiftaw

    Joined:
    Jan 31, 2005
    Location:
    Omaha, NE, USA
    #11
    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

    Jasonbot

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

    Joined:
    Jul 5, 2007
    Location:
    Northwestern Illinois
    #13
    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.

    Gertrude
     
  13. tominated macrumors 68000

    tominated

    Joined:
    Jul 7, 2006
    Location:
    Queensland, Australia
    #14
    wow. i think i just had a mini stroke.

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

    Joined:
    Mar 21, 2006
    Location:
    Hoosiertown
    #15
    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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