Question
1. An average American household uses about 1.04×104%0D%0A1.04%0D%0A×%0D%0A10%0D%0A4%0D%0A kWh (kilowatt hours) of electricity a year. If a power station generates 2.496×1010%0D%0A2.496%0D%0A×%0D%0A10%0D%0A10%0D%0A kWh per year, how many households can it serve? Write your answer in scientific notation, expressed to the exact decimal place.(1 point)
2. There are about 1.6×10^3%0D%0A1.6%0D%0A×%0D%0A10%0D%0A3%0D%0A meters in a mile. About how many miles are there in 3.52×10^7%0D%0A3.52%0D%0A×%0D%0A10%0D%0A7%0D%0A meters? Write your answer in scientific notation, expressed to the exact decimal place.(1 point)
3. An online data storage facility has 1.326×10^13%0D%0A1.326%0D%0A×%0D%0A10%0D%0A13%0D%0A bytes of storage available. It has 2.6×10^4%0D%0A2.6%0D%0A×%0D%0A10%0D%0A4%0D%0A customers. How many bytes of storage can each customer use? Write your answer in scientific notation, expressed to the exact decimal place.(1 point)%0D%0A$$
4. A public aquarium is being built to contain neon tetras. Each neon tetra needs 1.25 gallons of water. The aquarium will contain 1×10^5%0D%0A1%0D%0A×%0D%0A10%0D%0A5%0D%0A gallons of water. How many tetras can it house? Write the answer in scientific notation.(1 point)
5. A feather weighs 0.0082 g. How many feathers would you need to make a weight of 4.1×10^3%0D%0A4.1%0D%0A×%0D%0A10%0D%0A3%0D%0A g? Write the answer in scientific notation.(1 point)
2. There are about 1.6×10^3%0D%0A1.6%0D%0A×%0D%0A10%0D%0A3%0D%0A meters in a mile. About how many miles are there in 3.52×10^7%0D%0A3.52%0D%0A×%0D%0A10%0D%0A7%0D%0A meters? Write your answer in scientific notation, expressed to the exact decimal place.(1 point)
3. An online data storage facility has 1.326×10^13%0D%0A1.326%0D%0A×%0D%0A10%0D%0A13%0D%0A bytes of storage available. It has 2.6×10^4%0D%0A2.6%0D%0A×%0D%0A10%0D%0A4%0D%0A customers. How many bytes of storage can each customer use? Write your answer in scientific notation, expressed to the exact decimal place.(1 point)%0D%0A$$
4. A public aquarium is being built to contain neon tetras. Each neon tetra needs 1.25 gallons of water. The aquarium will contain 1×10^5%0D%0A1%0D%0A×%0D%0A10%0D%0A5%0D%0A gallons of water. How many tetras can it house? Write the answer in scientific notation.(1 point)
5. A feather weighs 0.0082 g. How many feathers would you need to make a weight of 4.1×10^3%0D%0A4.1%0D%0A×%0D%0A10%0D%0A3%0D%0A g? Write the answer in scientific notation.(1 point)
Answers
GPT-4o mini
Let's solve each question step by step:
1. **Households Served by Power Station**
- Average usage per household: \(1.04 \times 10^4 \) kWh.
- Total generation by power station: \(2.496 \times 10^{10} \) kWh.
- To find the number of households it can serve, divide total kWh by kWh per household:
\[
\text{Number of households} = \frac{2.496 \times 10^{10}}{1.04 \times 10^{4}} = \frac{2.496}{1.04} \times 10^{10 - 4} = 2.4 \times 10^6
\]
2. **Miles from Meters**
- Meters in a mile: \(1.6 \times 10^3 \).
- Meters to convert: \(3.52 \times 10^7 \).
- To find the number of miles, divide the total meters by meters per mile:
\[
\text{Miles} = \frac{3.52 \times 10^7}{1.6 \times 10^3} = \frac{3.52}{1.6} \times 10^{7 - 3} = 2.2 \times 10^4
\]
3. **Bytes of Storage per Customer**
- Total storage available: \(1.326 \times 10^{13} \) bytes.
- Number of customers: \(2.6 \times 10^4 \).
- Divide total bytes by number of customers:
\[
\text{Bytes per customer} = \frac{1.326 \times 10^{13}}{2.6 \times 10^4} = \frac{1.326}{2.6} \times 10^{13 - 4} = 0.51 \times 10^9 = 5.1 \times 10^8
\]
4. **Neon Tetras in Aquarium**
- Gallons for each tetra: \(1.25 \).
- Total gallons in the aquarium: \(1 \times 10^5 \).
- Divide total gallons by gallons per tetra:
\[
\text{Tetras} = \frac{1 \times 10^5}{1.25} = 0.8 \times 10^5 = 8 \times 10^4
\]
5. **Feathers for a Specific Weight**
- Weight of one feather: \(0.0082 \) g.
- Desired weight: \(4.1 \times 10^3 \) g.
- Divide total weight by weight of one feather:
\[
\text{Feathers needed} = \frac{4.1 \times 10^3}{0.0082} = \frac{4.1}{0.0082} \times 10^{3} = 500 \times 10^{3} = 5 \times 10^5
\]
### Final Answers
1. \(2.4 \times 10^6\)
2. \(2.2 \times 10^4\)
3. \(5.1 \times 10^8\)
4. \(8 \times 10^4\)
5. \(5 \times 10^5\)
1. **Households Served by Power Station**
- Average usage per household: \(1.04 \times 10^4 \) kWh.
- Total generation by power station: \(2.496 \times 10^{10} \) kWh.
- To find the number of households it can serve, divide total kWh by kWh per household:
\[
\text{Number of households} = \frac{2.496 \times 10^{10}}{1.04 \times 10^{4}} = \frac{2.496}{1.04} \times 10^{10 - 4} = 2.4 \times 10^6
\]
2. **Miles from Meters**
- Meters in a mile: \(1.6 \times 10^3 \).
- Meters to convert: \(3.52 \times 10^7 \).
- To find the number of miles, divide the total meters by meters per mile:
\[
\text{Miles} = \frac{3.52 \times 10^7}{1.6 \times 10^3} = \frac{3.52}{1.6} \times 10^{7 - 3} = 2.2 \times 10^4
\]
3. **Bytes of Storage per Customer**
- Total storage available: \(1.326 \times 10^{13} \) bytes.
- Number of customers: \(2.6 \times 10^4 \).
- Divide total bytes by number of customers:
\[
\text{Bytes per customer} = \frac{1.326 \times 10^{13}}{2.6 \times 10^4} = \frac{1.326}{2.6} \times 10^{13 - 4} = 0.51 \times 10^9 = 5.1 \times 10^8
\]
4. **Neon Tetras in Aquarium**
- Gallons for each tetra: \(1.25 \).
- Total gallons in the aquarium: \(1 \times 10^5 \).
- Divide total gallons by gallons per tetra:
\[
\text{Tetras} = \frac{1 \times 10^5}{1.25} = 0.8 \times 10^5 = 8 \times 10^4
\]
5. **Feathers for a Specific Weight**
- Weight of one feather: \(0.0082 \) g.
- Desired weight: \(4.1 \times 10^3 \) g.
- Divide total weight by weight of one feather:
\[
\text{Feathers needed} = \frac{4.1 \times 10^3}{0.0082} = \frac{4.1}{0.0082} \times 10^{3} = 500 \times 10^{3} = 5 \times 10^5
\]
### Final Answers
1. \(2.4 \times 10^6\)
2. \(2.2 \times 10^4\)
3. \(5.1 \times 10^8\)
4. \(8 \times 10^4\)
5. \(5 \times 10^5\)
PERFECT
A rectangular park has an area of 1.36×108 ft2 . The length of the park is 1.6×104 ft. Divide the area by the length to find the width of the park.(1 point)%0D%0AResponses%0D%0A%0D%0A8.5×102 ft.%0D%0A8.5 times 10 squared ft.%0D%0A%0D%0A8.5×104 ft.%0D%0A8.5 times 10 superscript 4 baseline ft.%0D%0A%0D%0A8.5×105 ft.%0D%0A8.5 times 10 superscript 5 baseline ft.%0D%0A%0D%0A8.5×103 ft.
2. Divide 3.3×104 by 5.5×107%0D%0A5.5%0D%0A×%0D%0A10%0D%0A7%0D%0A.(1 point)%0D%0AResponses%0D%0A%0D%0A6×10−3%0D%0A6%0D%0A×%0D%0A10%0D%0A−%0D%0A3%0D%0A6 times 10 to the negative 3 power%0D%0A%0D%0A6×10−4%0D%0A6%0D%0A×%0D%0A10%0D%0A−%0D%0A4%0D%0A6 times 10 to the negative 4 power%0D%0A%0D%0A6×10−6%0D%0A6%0D%0A×%0D%0A10%0D%0A−%0D%0A6%0D%0A6 times 10 to the negative 6 power%0D%0A%0D%0A6×10−5
3. A city lunch program for seniors received a grant of 1.925×106 dollars. Divide that figure by the cost of $2.75 per lunch to find out how many senior lunches the grant can provide. Write the answer in scientific notation.(1 point)%0D%0AResponses%0D%0A%0D%0A0.7×105%0D%0A 0.7 times 10 superscript 5 baseline%0D%0A%0D%0A7×106%0D%0A 7 times 10 superscript 6 baseline%0D%0A%0D%0A7×105%0D%0A7 times 10 superscript 5 baseline%0D%0A%0D%0A0.7×106
4. Solomon needs to distribute 10.5 gallons of perfume among 3.5×102 containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.(1 point)%0D%0AResponses%0D%0A%0D%0A0.35×10−1%0D%0A 0.35 times 10 superscript negative 1 baseline%0D%0A%0D%0A3×10−1%0D%0A 3 times 10 superscript negative 1 baseline%0D%0A%0D%0A3×102%0D%0A 3 times 10 squared%0D%0A%0D%0A3×10−2
5. A large pavilion is made of 2.967×105 bricks. There are 6.9 bricks per square foot. How many square feet is the pavilion? Write the answer in scientific notation.(1 point)%0D%0AResponses%0D%0A%0D%0A4.3×104%0D%0A4.3 times 10 superscript 4 baseline%0D%0A%0D%0A4.3×105%0D%0A 4.3 times 10 superscript 5 baseline%0D%0A%0D%0A2.33×105%0D%0A 2.33 times 10 superscript 5 baseline%0D%0A%0D%0A0.43×104
A rectangular park has an area of 1.36×108 ft2 . The length of the park is 1.6×104 ft. Divide the area by the length to find the width of the park.(1 point)%0D%0AResponses%0D%0A%0D%0A8.5×102 ft.%0D%0A8.5 times 10 squared ft.%0D%0A%0D%0A8.5×104 ft.%0D%0A8.5 times 10 superscript 4 baseline ft.%0D%0A%0D%0A8.5×105 ft.%0D%0A8.5 times 10 superscript 5 baseline ft.%0D%0A%0D%0A8.5×103 ft.
2. Divide 3.3×104 by 5.5×107%0D%0A5.5%0D%0A×%0D%0A10%0D%0A7%0D%0A.(1 point)%0D%0AResponses%0D%0A%0D%0A6×10−3%0D%0A6%0D%0A×%0D%0A10%0D%0A−%0D%0A3%0D%0A6 times 10 to the negative 3 power%0D%0A%0D%0A6×10−4%0D%0A6%0D%0A×%0D%0A10%0D%0A−%0D%0A4%0D%0A6 times 10 to the negative 4 power%0D%0A%0D%0A6×10−6%0D%0A6%0D%0A×%0D%0A10%0D%0A−%0D%0A6%0D%0A6 times 10 to the negative 6 power%0D%0A%0D%0A6×10−5
3. A city lunch program for seniors received a grant of 1.925×106 dollars. Divide that figure by the cost of $2.75 per lunch to find out how many senior lunches the grant can provide. Write the answer in scientific notation.(1 point)%0D%0AResponses%0D%0A%0D%0A0.7×105%0D%0A 0.7 times 10 superscript 5 baseline%0D%0A%0D%0A7×106%0D%0A 7 times 10 superscript 6 baseline%0D%0A%0D%0A7×105%0D%0A7 times 10 superscript 5 baseline%0D%0A%0D%0A0.7×106
4. Solomon needs to distribute 10.5 gallons of perfume among 3.5×102 containers. How many gallons of perfume will be in each container? Write the answer in scientific notation.(1 point)%0D%0AResponses%0D%0A%0D%0A0.35×10−1%0D%0A 0.35 times 10 superscript negative 1 baseline%0D%0A%0D%0A3×10−1%0D%0A 3 times 10 superscript negative 1 baseline%0D%0A%0D%0A3×102%0D%0A 3 times 10 squared%0D%0A%0D%0A3×10−2
5. A large pavilion is made of 2.967×105 bricks. There are 6.9 bricks per square foot. How many square feet is the pavilion? Write the answer in scientific notation.(1 point)%0D%0AResponses%0D%0A%0D%0A4.3×104%0D%0A4.3 times 10 superscript 4 baseline%0D%0A%0D%0A4.3×105%0D%0A 4.3 times 10 superscript 5 baseline%0D%0A%0D%0A2.33×105%0D%0A 2.33 times 10 superscript 5 baseline%0D%0A%0D%0A0.43×104
GPT-4o mini
Let's solve each question step by step.
### Question 1: Find the Width of the Park
Given:
- Area of the park = \(1.36 \times 10^8\) ft²
- Length of the park = \(1.6 \times 10^4\) ft
To find the width, divide the area by the length:
\[
\text{Width} = \frac{1.36 \times 10^8}{1.6 \times 10^4}
\]
Calculating:
1. Divide the coefficients:
\[
\frac{1.36}{1.6} = 0.85
\]
2. Subtract the exponents:
\[
10^{8 - 4} = 10^4
\]
Combining gives:
\[
\text{Width} = 0.85 \times 10^4 = 8.5 \times 10^3 \text{ ft}
\]
### Question 2: Divide \(3.3 \times 10^4\) by \(5.5 \times 10^7\)
\[
\frac{3.3 \times 10^4}{5.5 \times 10^7} = \frac{3.3}{5.5} \times 10^{4 - 7}
\]
Calculating:
1. Divide the coefficients:
\[
\frac{3.3}{5.5} = 0.6
\]
2. Subtract the exponents:
\[
10^{-3}
\]
Combining gives:
\[
\text{Result} = 0.6 \times 10^{-3} = 6 \times 10^{-4}
\]
### Question 3: Divide Grant Amount by Cost per Lunch
Given: Grant = \(1.925 \times 10^6\) dollars, Cost per lunch = 2.75 dollars.
To find the number of lunches:
\[
\text{Number of lunches} = \frac{1.925 \times 10^6}{2.75}
\]
Calculating:
1. First, convert 2.75 into scientific notation (approximately \(2.75 \approx 2.75 \times 10^0\)).
2. Divide the coefficients:
\[
\frac{1.925}{2.75} \approx 0.7
\]
3. The exponent remains \(10^6\):
\[
\text{Result} = 0.7 \times 10^6 = 7 \times 10^5
\]
### Question 4: Distributing Perfume
Given: Total perfume = 10.5 gallons, Number of containers = \(3.5 \times 10^2\).
Find amount per container:
\[
\text{Amount per container} = \frac{10.5}{3.5 \times 10^2} = \frac{10.5}{3.5} \times 10^{-2}
\]
Calculating:
1. \(10.5 \div 3.5 = 3\)
2. Result:
\[
\text{Result} = 3 \times 10^{-1}
\]
### Question 5: Square Feet of the Pavilion
Given: Number of bricks = \(2.967 \times 10^5\) bricks, Bricks per square foot = 6.9 bricks.
To find square feet:
\[
\text{Square feet} = \frac{2.967 \times 10^5}{6.9}
\]
Calculating:
1. Divide coefficients:
\[
\frac{2.967}{6.9} \approx 0.43
\]
2. Keep the exponent:
\[
\text{Result} = 0.43 \times 10^5 = 4.3 \times 10^4
\]
### Final Answers
1. **Width of Park**: \(8.5 \times 10^3\) ft
2. **Result of Divide**: \(6 \times 10^{-4}\)
3. **Number of Lunches**: \(7 \times 10^5\)
4. **Amount per Container**: \(3 \times 10^{-1}\)
5. **Square Feet of Pavilion**: \(4.3 \times 10^4\) ft²
### Question 1: Find the Width of the Park
Given:
- Area of the park = \(1.36 \times 10^8\) ft²
- Length of the park = \(1.6 \times 10^4\) ft
To find the width, divide the area by the length:
\[
\text{Width} = \frac{1.36 \times 10^8}{1.6 \times 10^4}
\]
Calculating:
1. Divide the coefficients:
\[
\frac{1.36}{1.6} = 0.85
\]
2. Subtract the exponents:
\[
10^{8 - 4} = 10^4
\]
Combining gives:
\[
\text{Width} = 0.85 \times 10^4 = 8.5 \times 10^3 \text{ ft}
\]
### Question 2: Divide \(3.3 \times 10^4\) by \(5.5 \times 10^7\)
\[
\frac{3.3 \times 10^4}{5.5 \times 10^7} = \frac{3.3}{5.5} \times 10^{4 - 7}
\]
Calculating:
1. Divide the coefficients:
\[
\frac{3.3}{5.5} = 0.6
\]
2. Subtract the exponents:
\[
10^{-3}
\]
Combining gives:
\[
\text{Result} = 0.6 \times 10^{-3} = 6 \times 10^{-4}
\]
### Question 3: Divide Grant Amount by Cost per Lunch
Given: Grant = \(1.925 \times 10^6\) dollars, Cost per lunch = 2.75 dollars.
To find the number of lunches:
\[
\text{Number of lunches} = \frac{1.925 \times 10^6}{2.75}
\]
Calculating:
1. First, convert 2.75 into scientific notation (approximately \(2.75 \approx 2.75 \times 10^0\)).
2. Divide the coefficients:
\[
\frac{1.925}{2.75} \approx 0.7
\]
3. The exponent remains \(10^6\):
\[
\text{Result} = 0.7 \times 10^6 = 7 \times 10^5
\]
### Question 4: Distributing Perfume
Given: Total perfume = 10.5 gallons, Number of containers = \(3.5 \times 10^2\).
Find amount per container:
\[
\text{Amount per container} = \frac{10.5}{3.5 \times 10^2} = \frac{10.5}{3.5} \times 10^{-2}
\]
Calculating:
1. \(10.5 \div 3.5 = 3\)
2. Result:
\[
\text{Result} = 3 \times 10^{-1}
\]
### Question 5: Square Feet of the Pavilion
Given: Number of bricks = \(2.967 \times 10^5\) bricks, Bricks per square foot = 6.9 bricks.
To find square feet:
\[
\text{Square feet} = \frac{2.967 \times 10^5}{6.9}
\]
Calculating:
1. Divide coefficients:
\[
\frac{2.967}{6.9} \approx 0.43
\]
2. Keep the exponent:
\[
\text{Result} = 0.43 \times 10^5 = 4.3 \times 10^4
\]
### Final Answers
1. **Width of Park**: \(8.5 \times 10^3\) ft
2. **Result of Divide**: \(6 \times 10^{-4}\)
3. **Number of Lunches**: \(7 \times 10^5\)
4. **Amount per Container**: \(3 \times 10^{-1}\)
5. **Square Feet of Pavilion**: \(4.3 \times 10^4\) ft²
4 is 3x10^-2
GPT-4o mini
Apologies for any confusion in my previous response regarding Question 4. Let's clarify that calculation properly.
### Question 4: Distributing Perfume
You need to divide 10.5 gallons of perfume among \(3.5 \times 10^2\) containers.
To find out how many gallons of perfume will be in each container, you set up the division like this:
\[
\text{Amount per container} = \frac{10.5 \text{ gallons}}{3.5 \times 10^2 \text{ containers}}
\]
1. First, calculate the division of the coefficients:
\[
\frac{10.5}{3.5} = 3
\]
2. The denominator has a power of ten, so we subtract the exponent:
\[
3 \text{ (since } 10^0 \text{ is just } 1\text{)} \text{ and } 10^{-2}
\]
Thus,
\[
\text{Amount per container} = 3 \times 10^{-2} \text{ gallons}
\]
So, the correct answer is indeed:
**3 × 10^{-2} gallons**
Thank you for your patience, and I appreciate your understanding as we clarify these calculations! If you have any further questions, feel free to ask.
### Question 4: Distributing Perfume
You need to divide 10.5 gallons of perfume among \(3.5 \times 10^2\) containers.
To find out how many gallons of perfume will be in each container, you set up the division like this:
\[
\text{Amount per container} = \frac{10.5 \text{ gallons}}{3.5 \times 10^2 \text{ containers}}
\]
1. First, calculate the division of the coefficients:
\[
\frac{10.5}{3.5} = 3
\]
2. The denominator has a power of ten, so we subtract the exponent:
\[
3 \text{ (since } 10^0 \text{ is just } 1\text{)} \text{ and } 10^{-2}
\]
Thus,
\[
\text{Amount per container} = 3 \times 10^{-2} \text{ gallons}
\]
So, the correct answer is indeed:
**3 × 10^{-2} gallons**
Thank you for your patience, and I appreciate your understanding as we clarify these calculations! If you have any further questions, feel free to ask.