Chapter 5 : Repeating Decimals (A3 Repunits)

(May 25, 1997, April 16, 2008) [Japanese]


First, please see the following remarkable patterns

Computing the repeating sequences of 1/p for 2 ≤ p < 100, prime except p=2, 5.

Explanation for the repeating sequences of 1/p and factors of repunit (10n|1)/9 : 11...11, repetition of "1").

In order to understand this problem, please try to solve the following questions.


  1. How to compute a repeating sequence
  2. Property of pattern of repeating decimal
  3. How to find the fraction from the repeating sequence
  4. General case
  5. Remarkable patterns

Chapter 4
"Mathematician's Secret Room" Chapter 6
Additive Palindromicness of Natural Numbers
Chapter 4 (Japanese) index (Japanese) Chapter 6 (Japanese)

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Hisanori Mishima