an average American household uses about 1.04×10 power of 4KWH kWh of electricity a year if a power station generates 2.496×10 power of 10 kW per year. How many households can it serve write your answer in scientific notation express to the exact decimal place.

Answer 1

To find out how many average American households can be served by the power generated by the power station, we need to divide the total amount of electricity generated by the power station per year by the amount of electricity used by an average household per year.

1. The annual electricity generation from the power station is: \[ P = 2.496 \times 10^{10} \text{ kWh} \]

2. The annual electricity consumption of an average American household is: \[ H = 1.04 \times 10^{4} \text{ kWh} \]

3. To find the number of households that can be served, we calculate: \[ \text{Number of households} = \frac{P}{H} = \frac{2.496 \times 10^{10}}{1.04 \times 10^{4}} \]

4. Performing the division:

   • Step 1: Divide the coefficients: \[ \frac{2.496}{1.04} = 2.396153846 \]

   • Step 2: Subtract the exponents of 10 (keeping in mind that \( 10^{10} / 10^{4} = 10^{10-4} = 10^6 \)): \[ 10^{10 - 4} = 10^{6} \]

   • Step 3: Combine the results: \[ \text{Number of households} \approx 2.396153846 \times 10^{6} \]

5. Expressing this in scientific notation with the exact decimal: \[ 2.396153846 \times 10^{6} \]

So, the power station can serve approximately \( \mathbf{2.396153846 \times 10^{6}} \) households.