A nuclear reactor generates power at a steady rate of 1000 MW ....

The total energy produced by the reactor in $1 \text{ hour}$ is calculated using the relation between energy, power, and time:
$E = P \times t$

Given $P = 1000 \text{ MW} = 10^9 \text{ W}$ and $t = 1 \text{ hour} = 3600 \text{ s}$:
$E = 10^9 \times 3600 = 3.6 \times 10^{12} \text{ J}$

According to the mass-energy equivalence principle, $E = mc^2$.
The mass $m$ converted into energy is:
$m = \dfrac{E}{c^2}$
$m = \dfrac{3.6 \times 10^{12}}{(3 \times 10^8)^2}$
$m = \dfrac{3.6 \times 10^{12}}{9 \times 10^{16}}$
$m = 0.4 \times 10^{-4} \text{ kg} = 4 \times 10^{-5} \text{ kg}$

To convert this mass into milligrams:
$1 \text{ kg} = 10^3 \text{ g} = 10^6 \text{ mg}$
$m = 4 \times 10^{-5} \times 10^6 \text{ mg} = 40 \text{ mg}$

Answer: $40$