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QUESTION 18 How many square kilometers are equinalent to \( 28.5 \mathrm{~cm}^{2} \) ? A. \( 2.85 \times 10^{-4} \mathrm{~km}^{2} \) O. \( 2.85 \times 10^{11} \mathrm{~km}^{2} \) OC. \( 285 \mathrm{~km}^{2} \) O \( \mathrm{D}_{2.85} \times 10^{-6} \mathrm{~km}^{2} \) OE. \( 2.85 \times 10^{-9} \mathrm{~km}^{2} \)

Ask by Fowler Gibson. in the United States
Jan 30,2025

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Tutor-Verified Answer

Answer

The equivalent of \( 28.5 \, \text{cm}^2 \) in square kilometers is \( 2.85 \times 10^{-9} \, \text{km}^2 \).

Solution

To convert \( 28.5 \, \text{cm}^2 \) to square kilometers, we need to use the conversion factors between centimeters and kilometers. 1. **Conversion Factors**: - \( 1 \, \text{km} = 100,000 \, \text{cm} \) - Therefore, \( 1 \, \text{km}^2 = (100,000 \, \text{cm})^2 = 10^{10} \, \text{cm}^2 \) 2. **Conversion Calculation**: To convert \( 28.5 \, \text{cm}^2 \) to \( \text{km}^2 \), we can use the formula: \[ \text{Area in km}^2 = \frac{\text{Area in cm}^2}{10^{10}} \] Substituting the known value: \[ \text{Area in km}^2 = \frac{28.5}{10^{10}} \] 3. **Performing the Calculation**: Let's calculate this value. \[ \text{Area in km}^2 = 28.5 \times 10^{-10} \] This can be expressed in scientific notation as: \[ \text{Area in km}^2 = 2.85 \times 10^{-9} \, \text{km}^2 \] 4. **Final Answer**: Thus, the equivalent area in square kilometers for \( 28.5 \, \text{cm}^2 \) is: \[ \boxed{2.85 \times 10^{-9} \, \text{km}^2} \] The correct option is **OE. \( 2.85 \times 10^{-9} \mathrm{~km}^{2} \)**.

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To convert \( 28.5 \mathrm{~cm}^{2} \) to square kilometers, you need to remember that \( 1 \mathrm{~km}^{2} = 10^{10} \mathrm{~cm}^{2} \). So, you can perform the following calculation: \[ 28.5 \mathrm{~cm}^{2} \times \frac{1 \mathrm{~km}^{2}}{10^{10} \mathrm{~cm}^{2}} = 2.85 \times 10^{-9} \mathrm{~km}^{2}. \] And voilà! The correct answer is option E, \( 2.85 \times 10^{-9} \mathrm{~km}^{2} \). When converting units, it's good to use dimensional analysis: just keep track of your units and cancel them out as needed! This helps avoid common mistakes like misplacing decimal points or failing to keep the right factors in mind. Always double-check your conversions!

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