Rank 1 valuations that are not discrete on finite transcendental extensions of the rationals

Question

Suppose $K=\mathbb{Q}(X_1,\dots,X_n)$ is a purely transcendental extension of the rationals on finitely many indeterminates. Can anyone give an example of a rank $1$ valuation on $K$ that fails to be discrete?

If not, is there a theorem that shows that such a rank $1$ valuation must be discrete?

Answer 1

Example: $val(X_1^{e_1}X_2^{e_2})=e_1 + e_2 \sqrt{2}$.