An average American household uses about 1.04×10^64 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.
To find the number of households that can be served by the power station, we need to divide the total electricity generated by the power station by the electricity used by an average household.
The total electricity generated by the power station is 2.496×10^10 kWh per year.
The electricity used by an average household is 1.04×10^64 kWh per year.
Now, let's divide the total electricity generated by the power station by the electricity used by an average household:
(2.496×10^10 kWh) / (1.04×10^64 kWh)
To divide the numbers, we subtract the exponent in the denominator from the exponent in the numerator and divide the coefficients:
2.496 / 1.04 = 2.4
Now, to find the exponent, we subtract the exponent in the denominator from the exponent in the numerator:
10^10 / 10^64 = 10^(10-64) = 10^-54
Putting it all together, the power station can serve approximately 2.4 × 10^-54 households.
To find out how many households can be served by the power station, we need to divide the total amount of electricity generated by the power station by the amount used by an average American household.
Total electricity generated by the power station = 2.496×10^10 kWh
Electricity used by an average American household = 1.04×10^64 kWh
The number of households served is calculated as follows:
Number of households = (Total electricity generated) / (Electricity used by an average American household)
Number of households = (2.496×10^10 kWh) / (1.04×10^64 kWh)
Dividing the numbers and subtracting the exponents:
Number of households = (2.496 / 1.04) × 10^(10-64)
Simplifying the calculation:
Number of households = 0.240 × 10^(-54)
Expressing the answer in scientific notation, with the decimal in the appropriate place:
Number of households = 2.40 × 10^(-55)