# Number of Digits in Base k Expansion of Fractions

Number of Digits in Base k Expansion of Fractions

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 .

1/8=0.125

1/7=0.142857

5/6=0.83333

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q

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