An average American household uses about 1.04 x 104 kWh (kilowatt hours) of electricity a vear. If a power

Question

station generates 2.496 × 1010 kWh per year, how many households can it serve? Write your answer in scientific
notation, expressed to the exact decimal place.

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Answer 1

To find out how many average American households a power station can serve, we can use the formula:

\[ \text{Number of households} = \frac{\text{Total electricity generated by power station}}{\text{Electricity used by one household}} \]

We have:

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

Now, we can perform the division:

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

This can be simplified:

1. Divide the coefficients: \[ \frac{2.496}{1.04} = 2.39615384615 \approx 2.3962 \text{ (for more precision, you may keep more decimal places)} \]

2. Subtract the exponents (since we're dividing): \[ 10^{10 - 4} = 10^{6} \]

Now, combining these:

\[ \text{Number of households} = 2.3962 \times 10^{6} \]

So, the power station can serve approximately \( 2.3962 \times 10^{6} \) households.

Final answer in scientific notation:

\[ \boxed{2.3962 \times 10^{6}} \]