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Decimal expansion of a rational

Source: RMO 2018 P3

October 7, 2018
algebracombinatorics

Problem Statement

For a rational number rr, its *period* is the length of the smallest repeating block in its decimal expansion. for example, the number r=0.123123123...r=0.123123123... has period 33. If SS denotes the set of all rational numbers of the form r=abcdefgh‾r=\overline{abcdefgh} having period 88, find the sum of all elements in SS.
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