1. Not finding help here? Sign up for a free 30min 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!

Write # as a ratio of two integers

  1. Apr 18, 2004 #1
    Problem: Write the number 3.1415999999999... as a ratio of two integers.

    In my book, they have a similar example, but using 2.3171717... And this is how they solved that problem.

    2.3171717... = 2.3 + (17/10^3) + (17/10^5) + (17/10^7) + ...

    After the first term we have a geometric series with a = (17/10^3) and r = (1/10^2). Therefore:

    2.3171717... = 2.3 + [(17/10^3) / (1 - (1/10^2))] = 2.3 + [(17/1000)/(99/100)] = (23/10) + (17/990) = 1147/495 == 2.3171717...

    Thinking I could follow the similar steps with a different number, I thought it would work, but it really isn't.

    This is what I did:

    3.1415999999999... = 3.1415 + (99/10^6) + (99/10^8) + (99/10^10)

    a = (99/10^6) and r = (1/10^2)

    3.1415 + [(99/10^6) / (1 - (1/10^2))] = 3.1415 + [(99/1000000)/(99/100) = (31415/10000) + (1/10000) = (31416/10000) = 3.1416 which isn't 3.1415999999999...

    What am I doing wrong?

    Thanks
     
  2. jcsd
  3. Apr 18, 2004 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Actually, it is.


    P.S. any particular reason you were grouping the nines in pairs?
     
  4. Apr 18, 2004 #3
    technically, it is, but is that correct though? and no, there was no reason i paired them up.
     
  5. Apr 18, 2004 #4
    3.1416=3.141599999999... is very true. So any fractional representation of one is a representation of the other. In fact, that's how I would have solved this problem; I wouldn't have bothered with an infinite geometric series in this case.
     
  6. Apr 20, 2004 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor


    Techically it's true but is it correct??? Is that what you are asking?

    "True" is "true"- there is no "technically"! And if it's true, then it's correct.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Write # as a ratio of two integers
Loading...