Calculate the number of U-235 nuclei in 1 kg of natural uranium and the cost of electricity produced from it, given specific fission energy and cost per kWh.

The mass of natural uranium is $1.00 \text{ kg} = 1000 \text{ g}$.
Natural uranium contains $0.7\%$ Uranium-235.

$$\text{Mass of U-235} = 0.007 \times 1000 \text{ g} = 7 \text{ g}$$

The molar mass of U-235 is approximately $235 \text{ g/mol}$.

$$\text{Number of moles of U-235} = \frac{\text{Mass of U-235}}{\text{Molar mass of U-235}} = \frac{7 \text{ g}}{235 \text{ g/mol}}$$

Using Avogadro's number ($N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$):

$$\text{Number of U-235 nuclei} = \left(\frac{7}{235}\right) \text{ mol} \times 6.022 \times 10^{23} \text{ nuclei/mol}$$ $$\text{Number of U-235 nuclei} = 1.793787 \times 10^{22} \text{ nuclei}$$

Rounding to three significant figures:

$$\boxed{\text{1.79} \times 10^{22} \text{ nuclei}}$$

Energy released per U-235 fission $= 200 \text{ MeV}$.

$$\text{Total energy released (in MeV)} = (\text{Number of U-235 nuclei}) \times (\text{Energy per fission})$$ $$\text{Total energy released (in MeV)} = (1.793787 \times 10^{22}) \times (200 \text{ MeV})$$ $$\text{Total energy released (in MeV)} = 3.587574 \times 10^{24} \text{ MeV}$$

Using the conversion factor $1 \text{ MeV} = 1.602 \times 10^{-13} \text{ J}$:

$$\text{Total energy released (in J)} = (3.587574 \times 10^{24} \text{ MeV}) \times (1.602 \times 10^{-13} \text{ J/MeV})$$ $$\text{Total energy released (in J)} = 5.747809 \times 10^{11} \text{ J}$$

Using the conversion factor $1 \text{ kWh} = 3.6 \times 10^6 \text{ J}$:

$$\text{Energy in kWh} = \frac{5.747809 \times 10^{11} \text{ J}}{3.6 \times 10^6 \text{ J/kWh}}$$ $$\text{Energy in kWh} = 159661.36 \text{ kWh}$$

The cost of electrical energy is $60 \text{ frs per unit (kWh)}$.

$$\text{Total cost} = (\text{Energy in kWh}) \times (\text{Cost per kWh})$$ $$\text{Total cost} = (159661.36 \text{ kWh}) \times (60 \text{ frs/kWh})$$ $$\text{Total cost} = 9579681.6 \text{ frs}$$

Rounding to three significant figures:

$$\boxed{\text{9.58} \times 10^6 \text{ frs}}$$