Let \( m \) be a positive integer not divisible by 2 or 5. Prove that the decimal expansion of the fraction \( 1/m \) is periodic with period equal to the order of 10 modulo \( m \).

Let m be a positive integer not divisible by 2 or 5. We want to prove that the decimal expansion of…

Answered: Let m be a positive integer not…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let m be a positive integer not divisible by 2 or 5. Prove that the decimal expansion of the fraction 1/m is periodic with period equal to the order of 10 modulo m.