Results 1 to 2 of 2

Math Help - How many correct decimals required ...

  1. #1
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927

    How many correct decimals required ...

    Hello,
    somehow I'm stuck on a seemingly simple problem.

    Quote Originally Posted by Problem
    Given that n is an integer, and q is some rational 0 < q < 1 such that \sqrt{nq} yields an integer, can you set up a relationship linking the number of correct decimals of the nonrepeating part of q, and the error bound of \sqrt{nq} (hint : use orders of magnitude).
    Quote Originally Posted by Attempted proof
    Apart from the particular (and trivial) case k = 0, knowing k decimals of q gives q - 10^{-k} < a < q + 10^{-k}, so \sqrt{n\left (a - 10^{-k} \right )} < \sqrt{nq} < \sqrt{n\left (a + 10^{-k} \right )} which gives the error bound for a \approx q.
    Am I right ? Empirical tests seem to confirm this but I like to have more people look over my work because one always makes mistakes on his own.
    Last edited by Bacterius; May 17th 2010 at 04:22 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Made a little mistake, correcting ...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 15
    Last Post: July 29th 2011, 01:39 AM
  2. Replies: 2
    Last Post: January 20th 2010, 02:43 PM
  3. decimals
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: November 22nd 2009, 10:05 PM
  4. decimals
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 24th 2008, 03:08 PM
  5. Saying Decimals
    Posted in the Algebra Forum
    Replies: 7
    Last Post: February 5th 2008, 07:23 AM

Search Tags


/mathhelpforum @mathhelpforum