Repeating decimals and geometric applications

Connect infinite geometric series to repeating decimals, bouncing-ball distance and scaled areas. Practice converting recurring decimal blocks to exact fractions and translating repeated physical or geometric steps into a sum.

Ten single-select and multiselect problems build from familiar recurring decimals to mixed nonrepeating prefixes, stopping-time decisions and reverse modeling. Explanations carefully count the first drop, upward and downward travel, and the difference between length and area ratios. Rebound models are idealized; each prompt supplies its assumptions.