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Infinitely Repeating Decimal

Source: 1970 AHSME Problem 10

March 21, 2014
conicsellipsegeometrygeometric seriesAMC

Problem Statement

Let F=.48181⋯F=.48181\cdots be an infinite repeating decimal with the digits 88 and 11 repeating. When FF is written as a fraction in lowest terms, the denominator exceeds the numerator by
<spanclass=′latex−bold′>(A)</span>13<spanclass=′latex−bold′>(B)</span>14<spanclass=′latex−bold′>(C)</span>29<spanclass=′latex−bold′>(D)</span>57<spanclass=′latex−bold′>(E)</span>126<span class='latex-bold'>(A) </span>13\qquad<span class='latex-bold'>(B) </span>14\qquad<span class='latex-bold'>(C) </span>29\qquad<span class='latex-bold'>(D) </span>57\qquad <span class='latex-bold'>(E) </span>126
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