A chemist has 1.8 g of fullerene, C₆₀, whose molar mass is 720 g/mol…

Step 1. Molecules. $1.8\ \text{g} \div 720\ \text{g/mol} = 0.0025\ \text{mol}$ of $\text{C}_{60}$.

Step 2. Atoms in moles. $0.0025\ \text{mol} \times 60 = 0.15\ \text{mol}$ of carbon atoms. The quick way gives the same: $1.8\ \text{g} \div 12\ \text{g/mol} = 0.15\ \text{mol}$.

Step 3. Number of atoms. $0.15\ \text{mol} \times 6.022 \times 10^{23}\ \text{mol}^{-1} = 9.03 \times 10^{22}$ atoms.