Classify the following as: Weak or strong acid, weak or strong base, salt (from weak/strong acid and base). If appropriate, split the formula into its component ions.

HNO3

So far, all I have is:

HNO3 + H2O -> NO3^- + H3O^+

And I know HNO3 is a strong acid. What would I do next?

You have HNO3 correct although I would not react it with water; the question states to split it so I would write
HNO3==> H^+ + NO3^-
You didn't post the other acids/bases/salts.

No, I have to classify them was weak bases/acids, salts, etc. We were told to write the appropriate expression with water. So that's why I reacted it with that. So I need to use my expression to classify them.

Also, how would I recognize a weak base?

OK if that's the instructions. You have classified HNO3 as a strong acid and that is correct. You still didn't write any other substance to classify. Read your post.

Oh wait, I was confused. I thought I had to split each thing into its forumla with water and then classify them all. Sorry about that.

I can classify the strong/weak acids and bases, but how would I know if something is a salt?

If it isn't an acid and it isn't a base, it is a salt. Weak acid and weak bases will have a Ka or a Kb listed in set of tables for them.

If that is necessary, then
HNO3 + H2O ==> H3O^+ + NO3^-
HNO3 is the acid; NO3^- is its conjugate base. H2O is the base and H3O^+ is its conjugate acid.

To determine whether a substance is a salt, you need to understand the definition of a salt. In chemistry, a salt is an ionic compound that is formed when an acid reacts with a base. It consists of positive and negative ions held together by electrostatic forces.

To identify a salt, you'll need to examine the formula and determine if it is an ionic compound. Ionic compounds usually consist of a metal cation and a nonmetal anion. Common examples of salts include sodium chloride (NaCl), potassium nitrate (KNO3), and calcium carbonate (CaCO3).

In the case of HNO3, it is a strong acid, as you correctly identified. When it reacts with water, HNO3 dissociates completely into H^+ and NO3^- ions. Since HNO3 is an acid and not a salt, you would categorize it as a strong acid rather than a salt.

If you have other substances to classify, please provide their formulas so we can continue the process.