Results 1 to 2 of 2

Thread: Prove that any number with a recurring decimal expansion is equal to a fraction

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    30

    Prove that any number with a recurring decimal expansion is equal to a fraction

    Can anyone prove that any number with a recurring decimal expansion is equal to a fraction?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    715
    Try to prove that if it is $\displaystyle 0.a_1 a_2 a_3 ... a_n a_1 a_2 a_3 ... a_n a_1 a_2 a_3 ... a_n ... $then it can be writen as a fraction : $\displaystyle \frac{ a_1 a_2 a_3 ... a_n}{999...9} $ or $\displaystyle \frac{ a_1 a_2 a_3 ... a_n}{ 10^n - 1 } $
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof that recurring number must be rational?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Jun 10th 2010, 04:20 AM
  2. Explain a recurring decimal
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jun 5th 2010, 11:47 AM
  3. Replies: 3
    Last Post: May 14th 2009, 08:38 PM
  4. Replies: 2
    Last Post: Mar 7th 2009, 07:57 PM
  5. Recurring decimal expansion
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: Mar 5th 2007, 10:36 AM

Search Tags


/mathhelpforum @mathhelpforum