Rational numbers - periodic decimal expansion

  • #1

Homework Statement



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.

Homework Equations



see above

The Attempt at a Solution



Can someone explain what the question means by (m, 10) = 1
 

Answers and Replies

  • #2
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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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