1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to do this using series. Rep as ratio of two integers

  1. Nov 18, 2013 #1
    1. The problem statement, all variables and given/known data
    Express the number as a ratio of integers.
    10.1(35) = 10.135353535 the part in the left in () is where is is over lined to indicate it is repeating



    2. Relevant equations


    Geometric series
    3. The attempt at a solution

    10.1(35) = 10.1 + .035 = (101)/ (1000) + (35/10^3 + 35/10^6......)

    = 101/1000 + ((35/1000)/(1-(1000)) = .1360350
    Clearly wrong. What did I mess up
     
  2. jcsd
  3. Nov 18, 2013 #2

    Mark44

    Staff: Mentor

    10.1 ≠ 101/1000.
     
  4. Nov 18, 2013 #3

    Mark44

    Staff: Mentor

    There's another way to go at this, as well.
    Let S = 10.1353535...

    Then 1000S = 10135.353535...
    and 10S = 101.353535...

    Subtract the 2nd equation from the first and solve for S.
     
  5. Nov 18, 2013 #4
    Yeah that is actually what I did but I did it different. I said that it was Because I thought that you had to move the decimal to the end of the first repeating number.So in my case I said 10.1(35) the I have to move it to after the 5 so I multiply by 1000. My two equations will read.

    S = 10.135353535
    1000x = 10135.353535
    Do the subtraction and you get 999x = 10125 So I ended up with 375/37
    Why did you have 10S I just had x
     
  6. Nov 18, 2013 #5

    Mark44

    Staff: Mentor

    No you don't. 10135.353535... - 10.135353535... ≠ 10125
    So that the repeating part lines up in both numbers.
     
  7. Nov 18, 2013 #6
    1000S = 10135.353535...
    10S = 101.353535..

    Subtract

    990S = 10034 ---> S = 5017/495
     
  8. Nov 18, 2013 #7

    Mark44

    Staff: Mentor

    That's more like it...

    And of course you can check by doing the division.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How to do this using series. Rep as ratio of two integers
Loading...