Divide in Scientific Notation Practice

Question

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Question
An average American household uses about 1.04×104 kWh (kilowatt hours) of electricity a year. If a power 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.(1 point)
Remaining Attempts : 3

Answer 1

To find out how many households a power station can serve, you can divide the total electricity generated by the power station by the electricity consumption of an average household.

Given:

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

Now, let's perform the division:

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

To divide the powers of ten, subtract the exponents:

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

Calculating \( \frac{2.496}{1.04} \):

\[ \frac{2.496}{1.04} \approx 2.398 \]

Now, combining this with the power of ten:

\[ \approx 2.398 \times 10^{6} \]

Thus, the power station can serve approximately \(2.398 \times 10^{6}\) households.