Number Theory > Arithmetic > Fractions v
Number Theory > Arithmetic > Number Bases v

Midy's Theorem


If the period of a repeating decimal for , where p is prime and 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, , and 142 + 857 = 999.

 

Decimal Expansion, Repeating Decimal



References

Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, pp. 158-160, 1957.