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Number of Digits in Base k Expansion of Fractions

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Some fractions are terminating decimals, like ; some are periodic, with repeating digits in cycles, like ; and some are eventually periodic, like . The plot shows the number of digits in the base expansion of fractions with denominators up to and including , with the numerator varying from 1 to .

Contributed by: Enrique Zeleny (January 2008)
Open content licensed under CC BY-NC-SA

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