[H3O+]

The concentration in the water of a monoprotic acid, with the formula HX, is 0.10M. The concentration of the H₃O⁺ ion in this solution is 0.010M.

Is HX a strong or weak acid?

[My attempt]:
My understanding of this is that a strong acid is an acid that is completely ionized and a weak acid is an acid that is only partially ionized. So considering that we don't know what HX is, I have concluded that it must have had something to do with pH levels and concentration rather than being able to tell whether it will ionize completely or partially.

If so I found that the pH:

pH = -log (-0.010) = 2

This indicates that it's a  pretty strong acid right?

However, a sufficiently concentrated weak acid can still produce a low pH reading, and a very diluted strong acid can still produce a high pH reading.

The question gave the concentration of the acid in the water, saying that it is 0.10M. Is that concentrated or diluted? This is where I kind of got stuck. I don't know where I can proceed from here.

Thanks in advance.

[Corribus]

My understanding of this is that a strong acid is an acid that is completely ionized and a weak acid is an acid that is only partially ionized.

This is the usual formal definition. Then you went and confused yourself by calculating pH. pH has nothing to do with the strong/weak acid concept. A strong acid at very low concentration can have a higher pH than a weak acid at very high concentration. (Why?)

The question is a little ambiguous as worded. When you say "the concentration in the water of a monoprotic acid, with the formula HX, is 0.10M", I'm assuming you mean that the initial concentration (before any dissociation) is 0.10M.

First, it is always good to write out a reaction equation.

Next, if HX is a strong acid (it doesn't matter what X is) and you start with 0.1 M, what do you expect the concentrations of HX and the dissociation products to be at equilibrium? Keeping mind you defined a strong acid as one that is (approximately) fully dissociated at equilibrium. You should be able to do this in your head but if you need to, make an ICE table.

This should tell you the answer.

Note that if you meant that the concentration of HX is 0.1M at equilibrium, this changes the rationale a bit but ultimately not the answer as to whether the acid is strong or weak.