The strategy here would be to convert mass to moles and then from moles to the number of atoms.
100.0 g of iron(iii) oxide, or Fe2O3, has a molar mass of 159.687 g/mol. To convert the mass into the number of moles, divide the mass by the molar mass: (100.0 g)(159.687) = 0.6262 moles Fe2O3.
1 mole of any substance is, by definition, equal to 6.022 • 10^23 units of that substance. So to compute the number atoms contained in 0.6262 moles of Fe2O3, multiply (0.6262)(6.022 • 10^23) = 3.771 • 10^23 atoms of iron(iii) oxide, which is your answer (given to four significant figures).
