Here's how to determine the oxidation numbers in chromium(III) oxide (Cr₂O₃):

* Oxygen's Oxidation Number: Oxygen almost always has an oxidation number of -2 in compounds.

* Chromium's Oxidation Number: We know the overall charge of the compound is 0 (it's neutral). Let 'x' represent the oxidation number of chromium. We can set up an equation:

2(x) + 3(-2) = 0

2x - 6 = 0

2x = 6

x = +3

Therefore, the oxidation number of chromium in chromium(III) oxide is +3, and the oxidation number of oxygen is -2.