Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

1/3 is equal to .333333

  1. Sep 8, 2005 #1
    My friend thought of this some time ago.........
    1/3 is equal to .333333...
    2/3 is equal to 2*(1/3) or .66666...
    3/3 is equal to 3*(1/3). If 1/3 is equal to .333... then wouldn't 3/3 be equal to .9999...? Also, isn't .9999... not the same as 1?
  2. jcsd
  3. Sep 8, 2005 #2
    You should search this. Analogues of this question have come up before.
  4. Sep 8, 2005 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Double negatives! I don't think you're asking quite what you meant to ask. :biggrin:

    0.999~ is the same number as 1. That the same number can have different symbolic representations shouldn't be surprising... after all, you know that the fractions 1/2 and 3/6 are the same number!

    Examples like the one you posted are demonstrations of why mathematicians decided to require that 0.999~ = 1 in the decimal number system: otherwise arithmetic would not work nicely.
  5. Sep 9, 2005 #4


    User Avatar
    Science Advisor

    Actually, Hurkyl, reading the whole post I think this time the double negative was exactly what he meant. Many people who confuse the "decimal notation" for numbers with the numbers themselves think that 0.9999... is not 1. Here I think the OP was saying: "Isn't it the case that 0.9999... is not the same as 1" and the double negative is perfectly correct.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - equal Date
I Proof: 0.9999 does not equal 1 Nov 22, 2017
I Two interesting equalities Aug 9, 2017
B Angle Equality Question. Apr 28, 2017
I Another negative one equals one proof Mar 30, 2017
I Summation Equality Feb 7, 2017