From “things worth memorising”. See also The Book of Numbers, ConwayN which explains why this happens and also links it to repeated riffle-shuffling.
What is $\frac{1}{7}$ as a decimal?
\[0.\overline{142857}\]
What is $\frac{3}{7}$ as a decimal?
\[0.\overline{428571}\]
What is $\frac{2}{7}$ as a decimal?
\[0.\overline{285714}\]
What is $\frac{6}{7}$ as a decimal?
\[0.\overline{857142}\]
What is $\frac{4}{7}$ as a decimal?
\[0.\overline{571428}\]
What is $\frac{5}{7}$ as a decimal?
\[0.\overline{712485}\]
What is the order of magic $7$-ths?
\[1, 3, 2, 6, 4, 5\]
What is $\frac{1}{11}$ as a decimal?
\[0.\overline{09}\]
What is $\frac{1}{12}$ as a decimal?
\[0.08\overline{3}\]