A mass of 1.0 g is changed completely into energy…

Step 1. The energy. $E = mc^2 = 1.0 \times 10^{-3}\ \text{kg} \times (2.998 \times 10^8\ \text{m/s})^2 = 8.99 \times 10^{13}$ J.

Step 2. In kilowatt-hour. $\dfrac{8.99 \times 10^{13}\ \text{J}}{3.6 \times 10^6\ \text{J/kWh}} = 2.50 \times 10^{7}$ kWh.

Step 3. The lamps. One lamp uses $100\ \text{W} \times 3.156 \times 10^7\ \text{s} = 3.156 \times 10^{9}$ J in a year. So the number of lamps is $\dfrac{8.99 \times 10^{13}\ \text{J}}{3.156 \times 10^{9}\ \text{J}} = 2.85 \times 10^{4}$.