Some salts are not fully dissociated in solution.
This acidic strength means that even at low pH the acid is fully dissociated.
It has also been proposed that weak acids such as acetic acid, which are not fully dissociated at physiological pH values, can penetrate taste cells and thereby elicit an electrical response.
A weak electrolyte is one that is not fully dissociated.
Strong acids are said to be fully dissociated.
Zinc salts are usually fully dissociated in aqueous solution.
It's still acidic, just not as acidic as it would be if both acids were fully dissociated.
So, again, the difference between strong and weak is not how strongly acidic or basic the solution is, but rather whether the compound is fully dissociated or in equilibrium with its ions.
Potassium bromide, a typical ionic salt, is fully dissociated and near pH 7 in aqueous solution.
This means that the nitric acid in solution is fully dissociated except in extremely acidic solutions.