$m$-adic completion of the field of fraction

Question

Let $D$ be a domain and $K$ be its field of fraction. For each $n \in \mathbb{N}$, we know that $\{m^nK \}$ is the $m$-adic filtration on $K$. But I think $m^nK=K$. Am I right? I do not understand what the $m $-adic completion of $K $ is. Is there any informative refrences for more informaion for this? Thanks for any help.