Understanding Decimal Expansions - Why Some Numbers Repeat and Others Don't

Explore the mathematical principles behind decimal expansions in this 13-minute educational video that delves into why certain fractions result in repeating decimals while others terminate. Learn how prime factors determine decimal behavior, understand the fundamental differences between rational and irrational numbers, and discover the mathematical reasoning behind why irrational numbers neither repeat nor terminate. Master key concepts through clear explanations that progress from basic decimal expansions to more complex mathematical principles, concluding with a comprehensive recap of these numerical patterns and behaviors.