Results 1 to 3 of 3

Math Help - Repeating decimal

  1. #1
    Newbie
    Joined
    Mar 2007
    Posts
    7

    Repeating decimal

    I have to give the sum of p+q where p/q is the reduced fraction represented by the repeating decimal
    __
    1.36

    Not sure where to go for this one.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,851
    Thanks
    321
    Awards
    1
    Quote Originally Posted by amanda1 View Post
    I have to give the sum of p+q where p/q is the reduced fraction represented by the repeating decimal
    __
    1.36

    Not sure where to go for this one.
    Let x = 0.36363636363636....

    Let's multiply x by 100:
    100x = 36.3636363636363636....

    Now let's subtract x from this:
    100x - x = 36.3636363636363636... - 0.36363636363636... = 36

    99x = 36

    x = 36/99 = 4/11

    So 1.363636363636... = 1 + 4/11 = 15/11

    Thus p = 15 and q = 11.

    Thus p + q = 26.

    Note: Since 15/11 = 30/22, p + q could also be 52. Your answer is not unique.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,685
    Thanks
    616
    Hello, Amanda!

    A slightly different approach . . .


    Find the sum p+q where p/q is the reduced fraction
    represented by the repeating decimal 1.363636...

    Let N = 1.363636...

    Multiply by 100: .100N .= .136.363636...
    . . . Subtract N: . . . N .= . . .1.363636...

    And we have: . . . 99N .= .135

    Therefore: .N .= .135/99 .= .15/11 . . . and .p + q .= .26

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. n repeating digit of decimal number
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: December 22nd 2011, 08:49 AM
  2. Expressing repeating decimal as fraction
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 30th 2011, 06:10 PM
  3. Repeating decimal help
    Posted in the Algebra Forum
    Replies: 5
    Last Post: September 28th 2009, 03:12 AM
  4. Series with repeating decimal
    Posted in the Calculus Forum
    Replies: 14
    Last Post: October 13th 2008, 04:49 PM
  5. non-repeating decimal
    Posted in the Algebra Forum
    Replies: 2
    Last Post: July 18th 2007, 08:53 PM

Search Tags


/mathhelpforum @mathhelpforum