# 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.

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