  Let $\theta = [0; a_1, a_2, \dots]$ be the continued fraction expansion of an
irrational real number $\theta \in (0, 1)$. It is well-known that the
characteristic Sturmian word of slope $\theta$ is the limit of a sequence of
finite words $(M_k)_{k \ge 0}$, with $M_k$ of length $q_k$ (the denominator of
the $k$-th convergent to $\theta$) being a suitable concatenation of $a_k$
copies of $M_{k-1}$ and one copy of $M_{k-2}$. Our first result extends this to
any Sturmian word. Let $b \ge 2$ be an integer. Our second result gives the
continued fraction expansion of any real number $\xi$ whose $b$-ary expansion
is a Sturmian word ${\bf s}$ over the alphabet $\{0, b-1\}$. This extends a
classical result of B\"ohmer who considered only the case where ${\bf s}$ is
characteristic. As a consequence, we obtain a formula for the irrationality
exponent of $\xi$ in terms of the slope and the intercept of ${\bf s}$.
