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0.999 = 1 (Why?)

  1. Sep 26, 2005 #1
    0.999.... = 1 (Why?)

    Sorry to put such a basic question on here, but it's not for homework so I figured I'd post here.

    On these forums, I've saw the issue of .99... = 1 brought up before; however, I recently discovered it in Math class.

    My teacher said it equals one because it is being rounded; however, it actually doesn't equal one. I understand what she means; however, for some reason, I recall seeing a formula that mathematically proved .99... = 1 without rounding. Perhaps I am seeing things.
     
  2. jcsd
  3. Sep 26, 2005 #2
    That formula (or the closest thing to it, there is no formula) is in those fifty other threads.
     
  4. Sep 26, 2005 #3
    If your teacher said that 0.999... is only approximately 1, then she is wrong.
     
  5. Sep 26, 2005 #4

    Tom Mattson

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    Your teacher is wrong.

    Quickie demonstration:

    [tex]\frac{1}{3}=0.\bar{3}[/tex]

    [tex]3\left(\frac{1}{3}\right)=3(0.\bar{3})[/tex]

    [tex]1=0.\bar{9}[/tex]

    And if your teacher still thinks that [itex]0.\bar{9}=1[/itex], then ask him/her to try to find a real number between the two. It can't be done.
     
  6. Sep 26, 2005 #5

    Integral

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    This is not a new topic
     
  7. Sep 26, 2005 #6

    HallsofIvy

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    Not only is this not a new topic, it's a regular topic!

    My only objection to (1/3)= 0.33333... so 1= 0.999.... is that the same people who object to 1= 0.9999.... would also object to 3(0.3333....)= 0.999...- and they have a point. Proving one is equivalent to proving the other.

    The real point is that, by definition of a "base 10 number system", 0.999... means the infinite series .9+ .09+ .009+... which is a geometric series whose sum is 1.

    By the way, what grade is this teacher? And who is his/her principal/college president?!
     
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