Let $ξ$ be a real number and $b \ge 2$ an integer. We study the relationship between the irrationality exponent of $ξ$ and the subword complexity $p(n, \mathbf{x})$ of the $b$-ary expansion $\mathbf{x}$ of $ξ$, where $p(n, \mathbf{x})$ counts the number of distinct blocks of length $n$ in $\mathbf{x}$, for $n \ge 1$. If the irrationality exponent of $ξ$ is equal to $2$, which is the case for almost all real numbers $ξ$, we show that the limit superior of the sequence $(p(n, \mathbf{x}) / n)_{n \ge 1}$ is at least equal to 4/3. The proof is based on a careful study of the evolution of the Rauzy graphs of infinite words of low complexity.