While the expression of a single series with vinculum on top is adequate, the intention of the above expression is to show that the six cyclic permutations of 006993 can be obtained from this repeating decimal if we select six consecutive digits from the repeating decimal starting from different digits. The characterization of such numbers can be done using repeating decimals (and thus the related fractions), or directly.įor any integer coprime to 10, its reciprocal is a repeating decimal without any non-recurring digits. These specific integers, known as transposable integers, can be but are not always cyclic numbers. 076923 × 9 = 692307 (shifts cyclically two places left).128205 × 4 = 512820 (shifts cyclically one place right).142857 × 5 = 714285 (shifts cyclically one place right). The digits of some specific integers permute or shift cyclically when they are multiplied by a number n.
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