  In this note, we shall prove that the sum and the product of an algebraic
number $\alpha$ by the \textit{Liouville constant}
$L=\sum_{j=1}^{\infty}10^{-j!}$ is a $U$-number with type equals to the degree
of $\alpha$ (with respect to $\mathbb{Q}$). Moreover, we shall have that
  $\max\{w^{\ast}_n(\alpha L),w^{\ast}_n(\alpha + L)\}\leq 2m^2n+m-1$, for
$n=1,...,m-1$.
