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Math question

Discussion in 'The OT' started by dorfd1, Mar 18, 2009.

  1. Mar 18, 2009 #1 of 156
    dorfd1

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    Why does 1/3 + 2/3 = 1 but .33 repeating + .66 repeating = .99 repeating?
     
  2. Mar 18, 2009 #2 of 156
    spartanstew

    spartanstew Dry as a bone

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    Because 3+6=9
     
  3. Mar 18, 2009 #3 of 156
    dodge boy

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    1 over 3 plus 2 over 3 = 3 over 3 or 1

    (adding numbers with common denominators)
     
  4. Mar 18, 2009 #4 of 156
    dave29

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    .33 is not actually 1/3.....
     
  5. Mar 18, 2009 #5 of 156
    4HiMarks

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    .99999... repeating is equal to 1.
     
  6. Mar 18, 2009 #6 of 156
    dorfd1

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    1 does not repeat .99 repeating does repeat. so 1/3 + 2/3 does not equal .33 repeating + .66 repeating.
     
  7. Mar 18, 2009 #7 of 156
    dave29

    dave29 New Member

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    Not according to the laws of Infinity..........
     
  8. Mar 18, 2009 #8 of 156
    4HiMarks

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    What laws would that be?

    I can prove it, but you would need at least 2 semesters of calculus to understand the proof. Do you?
     
  9. Mar 18, 2009 #9 of 156
    4HiMarks

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    1/3 = .333... (repeating)
    2/3 = .666... (repeating)

    Equals added to equals are equal.
     
  10. Mar 18, 2009 #10 of 156
    Joe Bernardi

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    let x = 0.999999.... forever
    then 10x = 9.9999999...... forever

    then 10x minus x = 9.99999.... minus 0.99999....
    which equals exactly 9

    so 10x -x = 9x
    and 10x-x = 9

    so 9x = 9
    x = 1
     
  11. Mar 18, 2009 #11 of 156
    ghfiii

    ghfiii Mentor

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    how about proof
    x = 0.9...
    10x = 9.9... multiply both side by 10
    10x - x = 9.9... - 0.9... subtract second equation by first equation
    9x = 9
    x = 1 solve for x
    QED
    0.9... = 1
     
  12. Mar 18, 2009 #12 of 156
    LarryFlowers

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    :new_popco
     
  13. Mar 18, 2009 #13 of 156
    dorfd1

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    .33...+.66..=1?
     
  14. Mar 18, 2009 #14 of 156
    Brandon428

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    :group: Nerds unite! If you can't get the answer here,then you can't get it anywhere.
     
  15. Mar 18, 2009 #15 of 156
    spartanstew

    spartanstew Dry as a bone

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    Why .9999 (repeating) equals 1:

    .9999... is equal to 1 because no matter how small a difference
    between .9999... and 1 you ask for, enough 9s can be written to get
    within that difference. Since there is no other number that the sequence gets close to, if you're going to assign a value, the only sensible value is 1.

    Why .9999 (repeating) doesn't equal 1:

    Because 1/3 doesn't equal .3333 (repeating) either, but with each 3 added, the decimal gets closer to 1/3.

    In effect, while 1/3 + 2/3 = 1, .3333 + .6666 does not equal 1, because neither .3333 (repeating) nor .6666 (repeating) equals 1/3 or 2/3 respectively.
     
  16. Mar 18, 2009 #16 of 156
    4HiMarks

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    Make up your mind.

    .3333... (repeating infinitely) DOES equal 1/3. Just use the same proof as above for .9999... (repeating infinitely).

    It makes a big difference whether the sequence continues indefinitely (non-terminating) or ends at some point (terminating). otherwise, you run into one of Zeno's Paradoxes.
     
  17. Mar 18, 2009 #17 of 156
    dave29

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    Damn, I was just kidding with the infinity joke (kind of):rolleyes:
    and yes, I had 2 semesters of Calculus in high school......
     
  18. Mar 18, 2009 #18 of 156
    Richard King

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    I agree with Larry. ;)
     
  19. Mar 18, 2009 #19 of 156
    Greg Alsobrook

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    Why do you park on a driveway and drive on a parkway? :grin:
     
  20. Mar 18, 2009 #20 of 156
    Stuart Sweet

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    ...the answer: a difference that makes no difference, is no difference.
     

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