Express the repeating decimal as a fraction in lowest terms.
-A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only 70% as far as on the previous swing. How far will it swing altogether before coming to a complete stop? Round to the nearest inch when necessary.
A) 267 inches
B) 114 inches
C) 133 inches
D) 229 inches

Question

Quizplus · Accepted Answer

The total distance swung by the pendulum is a geometric series with the first term 80 and a common ratio of 0.7. The sum of an infinite geometric series is given by S = a / (1 - r), where a is the first term and r is the common ratio. Thus, S = 80 / (1 - 0.7) = 80 / 0.3 = 266.67, which rounds to 267 inches.

Express the Repeating Decimal as a Fraction in Lowest Terms