Problem 49 - Prealgebra

Question

The Google Earth map shows Yellowstone National Park. If the area of the park is roughly \(3,402\) square miles, how many acres does the park cover? (IMAGE CAN NOT COPY)

Step-by-Step Solution

Answer

Yellowstone National Park covers 2,177,280 acres.

Step 1: Understand the conversion factor between square miles and acres

In order to convert square miles to acres, you need to know the conversion factor: there are 640 acres in one square mile. This conversion factor will be essential to solving the problem.

Step 2: Multiply the area in square miles by the conversion factor

You multiply the area of Yellowstone National Park in square miles by the conversion factor to find the area in acres. The formula for this conversion is: \[ \text{Area in acres} = \text{Area in square miles} \times \text{Conversion factor} \].Plugging the numbers gives: \[ 3,402 \times 640 = 2,177,280 \] acres.

Key Concepts

Area Conversion

When discussing geographical areas, especially large ones like national parks, area conversion becomes a crucial aspect of understanding the size in different units of measurement.
Area conversion refers to the process of changing one unit of area measurement to another, allowing for easier comparison and understanding. The importance of area conversion is particularly evident when dealing with different units such as square miles and acres. Square miles are typically used for large expanses in countries like the United States. Acres, however, although smaller, are also widely used for land measurement, especially in agriculture. Converting these units helps when specific context or precision in certain units is required. Being familiar with these conversions can make geographic data more accessible and comprehensible across different fields and discussions.
Mastering area conversion is not only essential for academic purposes but also for practical real-world applications.

Square Miles to Acres

Understanding how to convert square miles to acres is a valuable skill, particularly when studying geography or planning land use. This specific conversion is frequently encountered in the United States. To convert from square miles to acres, use the conversion factor of 640. This means that one square mile is equivalent to 640 acres.
The formula can be remembered as simply multiplying the number of square miles by 640 to find the number of acres. For example, if you know that Yellowstone National Park covers an area of 3,402 square miles, you can calculate its area in acres using:

• Area in acres = Area in square miles × Conversion factor

Substituting the numbers gives:

• 3,402 × 640 = 2,177,280 acres

Remembering this straightforward conversion factor and method will enable you to perform similar conversions effectively whenever required.

Mathematical Problem Solving

The ability to solve mathematical problems efficiently is a fundamental skill that facilitates many day-to-day activities. When tackling a problem such as converting square miles to acres, it's important to follow clear and structured steps to achieve the correct solution. Here’s how you can approach mathematical problem solving:

• Understand the Problem: Make sure you comprehend the problem entirely. In our exercise, the task was to find how many acres are equivalent to a specified number of square miles.
• Identify Conversion Factors: Know the necessary conversion factors, such as the given 640 acres for one square mile.
• Apply the Conversion: Use the formula to calculate the required value. For instance, multiply the area in square miles by the conversion factor to get acres.
• Verify the Result: Check your calculations, ensuring the multiplication was performed correctly and that the conversion factor was applied properly.

By applying these steps, you can navigate similar mathematical problems with confidence and accuracy, ensuring that your conversion results are both reliable and comprehensible.