Decimal Expansion: Division and Periodicity

This lecture explores the decimal expansion of rational numbers, focusing on the case where the denominator is not a divisor of a power of 10. Through Euclidean division, the process of finding the decimal expansion is demonstrated, emphasizing the periodic nature of the result. Examples illustrate the iterative division process, highlighting the relationship between quotients and remainders. The lecture concludes with corollaries related to the irreducible fractions of numbers, showcasing the significance of understanding decimal expansions.