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Repeating decimal of 9's and 1.

Discussion in 'Other Discussions' started by 37818, Sep 14, 2021.

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  1. 37818

    37818 Well-Known Member

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    1/3 = .333 . . . the repeating decimal of 3's
    Now the the repeating decimal of 9's, .999 . . . there exists a disagreement as to whether it is equal to 1 or not.
     
    #1 37818, Sep 14, 2021
  2. JonC

    JonC Moderator
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    I vote no (it is not equal to 1, but would be treated as if it were).

    That said, I believe mathematically it is equal to 1. 1/3 × 3 = 1....so .33333 x .33333 has to equal 1.

    But philosophically it is just shy. :Biggrin
     
    #2 JonC, Sep 14, 2021
  3. Van

    Van Well-Known Member
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    The issue is not that it is ok to disregard the insignificant but on what constitutes insignificance. Lots of people present numbers as three significant figures and an exponent to locate the decimal either in front of or behind the figures. Thus .999 would be 9.99 x 10 to the minus 1.
     
    #3 Van, Sep 14, 2021
  4. Van

    Van Well-Known Member
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    Not according to my calculator... maybe closer to .11 (when you multiply with a number less than one, you reduce the amount...)
     
    #4 Van, Sep 14, 2021
  5. Salty

    Salty 20,000 Posts Club
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    How about - "it depends"
    What is :
    Task
    Conditions
    Standards
     
    #5 Salty, Sep 14, 2021
  6. JonC

    JonC Moderator
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    Yea. I meant 1/3 x 3 and .3333 x 3.
     
    #6 JonC, Sep 14, 2021
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  7. canadyjd

    canadyjd Well-Known Member

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    You math nerds are getting out of control.

    Next, you will go in a tangent, trying to discern the “sins” and “cosins” of the times.

    peace to you
     
    #7 canadyjd, Sep 14, 2021
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  8. 37818

    37818 Well-Known Member

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    There is tbe deference between the approximation of 1/3 and the infinite repeating decimal of .333 . . . .
    The disagreement is over the interpertation of the infinite repeating decimal of .999 . . . . It being equal to 1 or always an infinitesimal smaller than 1, where the infinitesimal greater than zero.
     
    #8 37818, Sep 16, 2021
  9. JonC

    JonC Moderator
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    What is the decimal form of 1/3 (1 divided by 3)?
     
    #9 JonC, Sep 16, 2021
  10. 37818

    37818 Well-Known Member

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    .111 . . . or 1/9 as a fraction. (1/3)/3.
     
    #10 37818, Sep 16, 2021
  11. JonC

    JonC Moderator
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    I mean what is the decimal form of 1/3?
     
    #11 JonC, Sep 16, 2021
  12. 37818

    37818 Well-Known Member

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    1/9 = .111 . . .
    2/9 = .222 . . .
    3/9 = 1/3 = .333 . . .
    4/9 = .444 . . .
    5/9 = .555 . . .
    6/9 = 2/3 = .666 . . .
    7/9 = .777 . . .
    8/9 = .888 . . .
    9/9 = 1 = .999 . . .
     
    #12 37818, Sep 16, 2021
  13. 37818

    37818 Well-Known Member

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    .333333333333333333 . . . etc.
     
    #13 37818, Sep 16, 2021
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  14. JonC

    JonC Moderator
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    Yep. 1/3 (which can be written 1÷3) = .3333.....


    What is .3333.... x 3?


    If A/B=C then A=BC.

    .999..... has to = 1
     
    #14 JonC, Sep 16, 2021
  15. RighteousnessTemperance&

    RighteousnessTemperance& Well-Known Member

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    Not arguing for the final value, but there is a succinct mathematical way to represent repeating decimals. Use a vinculum or overbar. Then, 1/3 would be 0.3 with a bar (vinculum) over the 3 to indicate it repeats infinitely. For thrice that, it would be 0.9 with a bar over the 9 to indicate the 9 repeats infinitely. I’d show it outright, but don’t know how here. And besides, everyone probably already knows this. :Wink
     
    #15 RighteousnessTemperance&, Sep 20, 2021
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