Quotients and Remainders Wheel

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Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: in the case of fractions of the form , the decimal digits of 1/7 appear cyclically

Snapshot 2: with the denominator 49, if is prime to 49, all fractions have the same cyclic arrangement of their digits; there are 42 such fractions and each has 42 digits in its period

Snapshot 3 and 4: other examples with long period and different selected digits

Snapshot 5: the longest period for a denominator less than 100

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