Relation To Repeating Decimals
Cyclic numbers are related to the recurring digital representations of unit fractions. A cyclic number of length L is the digital representation of
- 1/(L + 1).
Conversely, if the digital period of 1 /p (where p is prime) is
- p − 1,
then the digits represent a cyclic number.
For example:
- 1/7 = 0.142857 142857….
Multiples of these fractions exhibit cyclic permutation:
- 1/7 = 0.142857 142857…
- 2/7 = 0.285714 285714…
- 3/7 = 0.428571 428571…
- 4/7 = 0.571428 571428…
- 5/7 = 0.714285 714285…
- 6/7 = 0.857142 857142….
Read more about this topic: Cyclic Number
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