  For $A \subseteq \{1,2,\ldots\}$, we consider $R(A) = \{a/a' : a,a' \in A\}$.
If $A$ is the set of nonzero values assumed by a quadratic form, when is $R(A)$
dense in the $p$-adic numbers? We show that for a binary quadratic form $Q$,
$R(A)$ is dense in $\mathbb{Q}_{p}$ if and only if the discriminant of $Q$ is a
nonzero square in $\mathbb{Q}_{p}$, and for a quadratic form in at least three
variables, $R(A)$ is always dense in $\mathbb{Q}_{p}$. This answers a question
posed by several authors in 2017.
