Does any nonempty open set in $\mathbb{R}^n$ contains a point with rational coordinates?

Question

I would like to determine whether any nonempty open set in $\mathbb{R}^n$ contains a point with rational coordinates. The answer to this question seems to be confirmative because $\mathbb{Q}^n$ is dense in $\mathbb{R}^n$. But I don't know how to write down a proof. What I have known is that any nonempty open set cannot be finite. Help, please. Thank you.