If you dissolve 0.1 mol of formic acid in 1 L of water, ther esulting solution contains 0.004 mol of H₃O+. Based on this information, is formic acid a strong acid, or is it a weak acid? Please explain!

In an ideal case, the acid would completely protonate. such an acid would be a strong acid.  Dissociation of Formic acid looks like:

HCOOH + H₂O → COOH⁻ + H₃O⁺

one mole of formic acid should give one mole of Hydronium(H₃O⁺) ions

similarly, 0.1 moles of formic acid should produce 0.1 moles of hydronium ions. but we know that it is not the case, a much lesser amount is actually formed.

Which means that Formic acid did not completely dissociate into COOH⁻ and H⁺ ions.

Hence, Formic Acid is a weak acid