Reciprocal Expansions

The repeating "decimal" expansion of 1/n in each base.

The repeat period of 1/n in base b equals the multiplicative order of b mod n — so the same fraction can terminate in one base, have a short cycle in another, and a very long cycle in a third.

Fractions in green terminate (period 0). Fractions in red are full-reptend primes (period = n−1, the maximum). Fractions in blue have a palindromic repeating cycle. Repeating digits are shown in parentheses.

Select a radix below:

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