Recurring Parts of Multiples of One Fifty-Third

Theorem
The multiples of $\dfrac 1 {53}$ from $\dfrac 1 {53}$ to $\dfrac {52} {53}$ can be divided into $4$ sets of equal size:


 * one where the digits of the recurring part consists of a cyclic permutation of $01886 \, 79245 \, 283$


 * one where the digits of the recurring part consists of a cyclic permutation of $03773 \, 58490 \, 566$


 * one where the digits of the recurring part consists of a cyclic permutation of $07547 \, 16981 \, 132$


 * one where the digits of the recurring part consists of a cyclic permutation of $09433 \, 96226 \, 415$.