I am reading a paper by Serre, in which at some point he say
We extend the valuation $v$ from $K$ to $K^{sep}$; in this way we obtain a valuation on $K^{sep}$ with value group $v(K^{sep \times})=\mathbb{Q}$.
Here, $K$ is a number field complete with respect to $v$ a discrete valuation, and $K^{sep}$ is $K$'s separable closure. A separable closure is essentially the maximal Galois extension, or equivalently contains all separable elements in the algebraic closure of $K$. I am not entirely sure why that would yield $v(K^{sep \times})=\mathbb{Q}$? Like it could miss some elements of $\mathbb{Q}$, so I am not sure why it is exactly $\mathbb{Q}$.