An average American household uses about 1.04×10^4 kWh (kilowatt hours) of electricity a year. If a power station generates 2.496×10^10 kWh per year, how many households can it serve? Write your answer in scientific notation, expressed to the exact decimal place

Answer 1

To find out how many households a power station can serve, we can divide the total amount of electricity generated by the power station by the amount of electricity used by one average household.

Given:

• Electricity generated by the power station: \( 2.496 \times 10^{10} \) kWh
• Electricity used by one household: \( 1.04 \times 10^{4} \) kWh

We can calculate the number of households served as follows:

\[ \text{Number of households} = \frac{\text{Electricity generated}}{\text{Electricity per household}} = \frac{2.496 \times 10^{10}}{1.04 \times 10^{4}} \]

Now, we can perform the division:

\[ = \frac{2.496}{1.04} \times \frac{10^{10}}{10^{4}} \]

First, calculate \( \frac{2.496}{1.04} \):

\[ \frac{2.496}{1.04} = 2.4 \]

Then calculate \( \frac{10^{10}}{10^{4}} \):

\[ \frac{10^{10}}{10^{4}} = 10^{10-4} = 10^{6} \]

Now, combine the results:

\[ \text{Number of households} = 2.4 \times 10^{6} \]

Thus, the power station can serve \( \boxed{2.4 \times 10^{6}} \) households.