Converting Repeating Decimals to Fractions Using Geometric Series

Learn how to convert any repeating decimal into a fraction in this 21-minute mathematics video. Master the concept of infinite series and derive the geometric series formula to understand how repeating decimals can be expressed as geometric series. Follow along with clear explanations that progress from basic concepts of rational and irrational numbers through to practical applications, including how to convert common repeating decimals like 0.999... to 1 and 0.142857... to 1/7. Explore the fundamental relationship between decimal expansions and fractions through step-by-step demonstrations and mathematical proofs.