  In this paper we deal with a classical problem in elementary number theory,
namely repeating decimals. We show how the digits of the period of the decimal
representation of any fraction $\frac{k}{m}$, where $k$ and $m$ are positive
integers arbitrarily chosen, can be obtained relying upon the graphs associated
with the iteration of a certain map over the finite set $\{0, 1, \dots, 10n-2
\}$ for a suitable integer $n$, which depends on $m$. In the last section of
the paper we generalize the results to any arbitrary choice of the base $B \geq
2$ for the representation of the fraction $\frac{k}{m}$.
