An average American household uses about 1.04×104

Question

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)

There are about 1.6×103
meters in a mile. About how many miles are there in 3.52×107
meters? Write your answer in scientific notation, expressed to the exact decimal place.(1 point)

An online data storage facility has 1.326×1013
bytes of storage available. It has 2.6×104
customers. How many bytes of storage can each customer use? Write your answer in scientific notation, expressed to the exact decimal place.(1 point)

A public aquarium is being built to contain neon tetras. Each neon tetra needs 1.25 gallons of water. The aquarium will contain 1×105
gallons of water. How many tetras can it house? Write the answer in scientific notation.(1 point)

A feather weighs 0.0082 g. How many feathers would you need to make a weight of 4.1×103
g? Write the answer in scientific notation.(1 point)

Answer 1

Let's solve each problem step by step:

1. How many households can a power station serve? \[ \text{Households served} = \frac{\text{Power station's total kWh}}{\text{Average household kWh per year}} = \frac{2.496 \times 10^{10}}{1.04 \times 10^{4}} \] Performing the division: \[ = \frac{2.496}{1.04} \times 10^{10 - 4} = 2.4 \times 10^{6} \] So, the power station can serve \( \boxed{2.4 \times 10^{6}} \) households.

2. How many miles are there in \( 3.52 \times 10^{7} \) meters? \[ \text{Miles} = \frac{\text{Meters}}{\text{Meters per mile}} = \frac{3.52 \times 10^{7}}{1.6 \times 10^{3}} \] Performing the division: \[ = \frac{3.52}{1.6} \times 10^{7 - 3} = 2.2 \times 10^{4} \] So, there are \( \boxed{2.2 \times 10^{4}} \) miles in \( 3.52 \times 10^{7} \) meters.

3. How many bytes of storage can each customer use? \[ \text{Storage per customer} = \frac{\text{Total bytes}}{\text{Number of customers}} = \frac{1.326 \times 10^{13}}{2.6 \times 10^{4}} \] Performing the division: \[ = \frac{1.326}{2.6} \times 10^{13 - 4} = 0.510 \times 10^{9} = 5.10 \times 10^{8} \] So, each customer can use \( \boxed{5.10 \times 10^{8}} \) bytes of storage.

4. How many tetras can the aquarium house? \[ \text{Number of tetras} = \frac{\text{Total gallons}}{\text{Gallons per tetra}} = \frac{1 \times 10^{5}}{1.25} \] Performing the division: \[ = 8.0 \times 10^{4} \] So, the aquarium can house \( \boxed{8.0 \times 10^{4}} \) tetras.

5. How many feathers are needed to make a weight of \( 4.1 \times 10^{3} \) g? \[ \text{Number of feathers} = \frac{\text{Total weight}}{\text{Weight per feather}} = \frac{4.1 \times 10^{3}}{0.0082} \] Performing the division: \[ = \frac{4.1}{0.0082} \times 10^{3} = 500 \times 10^{3} = 5.0 \times 10^{5} \] So, you would need \( \boxed{5.0 \times 10^{5}} \) feathers.