Let's go through each problem step-by-step.
Problem 1: Finding the Width of the Park
Given:
- Area = \(1.36 \times 10^8 \text{ ft}^2\)
- Length = \(1.6 \times 10^4 \text{ ft}\)
To find the width (W), we use the formula for the area of a rectangle: \[ \text{Area} = \text{Length} \times \text{Width} \] So, we can rearrange it to find the width: \[ \text{Width} = \frac{\text{Area}}{\text{Length}} = \frac{1.36 \times 10^8}{1.6 \times 10^4} \]
Calculating this: \[ \text{Width} = \frac{1.36}{1.6} \times \frac{10^8}{10^4} = 0.85 \times 10^4 = 8.5 \times 10^3 \text{ ft} \]
Answer: 8.5×10³ ft.
Problem 2: Dividing Two Scientific Notations
Given:
- \(3.3 \times 10^4\)
- \(5.5 \times 10^7\)
We need to divide: \[ \frac{3.3 \times 10^4}{5.5 \times 10^7} = \frac{3.3}{5.5} \times \frac{10^4}{10^7} \]
Calculating this: \[ \frac{3.3}{5.5} = 0.6 \quad \text{and} \quad \frac{10^4}{10^7} = 10^{-3} \] So: \[ \frac{3.3 \times 10^4}{5.5 \times 10^7} = 0.6 \times 10^{-3} = 6 \times 10^{-4} \]
Answer: 6×10⁻⁴.
Problem 3: Dividing Total Grant by Cost per Lunch
Given:
- Grant = \(1.925 \times 10^6\)
- Cost per lunch = 2.75 dollars
To find the number of lunches: \[ \frac{1.925 \times 10^6}{2.75} \]
Calculating \(1.925 / 2.75\): Approximately \(0.7\).
Now put it in scientific notation: \[ 0.7 \times 10^6 = 7 \times 10^5 \]
Answer: 7×10⁵.
Problem 4: Distributing Perfume Among Containers
Given:
- Total perfume = 10.5 gallons
- Number of containers = \(3.5 \times 10^2\)
We need to find the amount in each container: \[ \frac{10.5}{3.5 \times 10^2} = \frac{10.5}{3.5} \times \frac{1}{10^2} \approx 3 \times 10^{-1} \]
Answer: 3×10⁻¹.
Problem 5: Finding Square Feet of the Pavilion
Given:
- Total bricks = \(2.967 \times 10^5\)
- Bricks per square foot = 6.9
To find the area in square feet: \[ \text{Area} = \frac{2.967 \times 10^5}{6.9} \]
Calculating \(2.967 / 6.9\) approximately equals to \(0.43\) (or \(4.3 \times 10^{-1}\)).
Hence: \[ \text{Area} = 4.3 \times 10^{5-1} = 4.3 \times 10^4 \]
Answer: 4.3×10⁴.
3 answers