Rational numbers - periodic decimal expansion

[saadsarfraz]

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

 

[slider142]

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.