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< Exercises

Finite geometric series word problems

Finn drops a ball straight down from a height of 88 decimeters (dm)(\text{dm}). With each bounce, it rises to 23\dfrac{2}{3} of the height of the previous bounce.
When it hits the ground the 10th10^\text{th} time, what is the total distance, in decimeters, that the ball has traveled?
Round your final answer the nearest hundredth.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
dm\text{dm}