midys theorem

Input interpretation

Midy's theorem

Definition

If the period of a repeating decimal for a/p, where p is prime and a/p is a reduced fraction, has an even number of digits, then dividing the repeating portion into halves and adding gives a string of 9s. For example, 1/7 = 0.142857^_, and 142 + 857 = 999.
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Related terms

decimal expansion | repeating decimal

Subject classifications

MathWorld

number bases | fractions
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