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Homework Help: Rational numbers - periodic decimal expansion

  1. Feb 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Let n/m be a positive rational number in lowest terms. By examining the long division algorithm, show that the decimal expansion of n/m is eventually periodic, and that the period divides phi(m). For simplicity,you may assume that (m, 10) = 1.

    2. Relevant equations

    see above

    3. The attempt at a solution

    Can someone explain what the question means by (m, 10) = 1
     
  2. jcsd
  3. Feb 21, 2009 #2
    I'm not sure what notation your book is using, but from the context, I assume (m, 10) = 1 means that the greatest common divisor of m and 10 is 1; ie., m and 10 are coprime.
     
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