To determine how many American households can be served by a power station that generates \(2.496 \times 10^{10}\) KWH of electricity per year, we first need to understand the electricity consumption of an average household.
The average annual electricity usage for an American household is given as:
\[ 1.04 \times 10^4 \text{ KWH} \]
Next, we need to calculate the number of households that can be served by the power station's total annual generation.
To find the number of households, we can use the formula:
\[ \text{Number of households} = \frac{\text{Total electricity generated by power station}}{\text{Electricity usage per household}} \]
Substituting the values:
\[ \text{Number of households} = \frac{2.496 \times 10^{10} \text{ KWH}}{1.04 \times 10^4 \text{ KWH}} \]
Now, simplifying this expression:
\[ \text{Number of households} = \frac{2.496 \times 10^{10}}{1.04 \times 10^4} \]
To divide the numbers:
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Divide the coefficients: \[ \frac{2.496}{1.04} \approx 2.4 \]
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Subtract the exponents: \[ 10^{10 - 4} = 10^6 \]
So,
\[ \text{Number of households} \approx 2.4 \times 10^6 \]
Thus, the power station can serve approximately \(2.4\) million households.
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