Decimal Expansion

The decimal expansion of a rational number eventually becomes periodic. As a
warm up, prove this. The assignment is to investigate the period of the decimal
expansion of 1/p , when p is a prime number .

Assignment

1. Compute the decimal expansions of 1/p for p < 100.
2. Explain the period of the decimal expansion of p^-1 in terms of modulo p
arithmetic .
3. Try to describe how the period varies with p probabilistically.