Problem 61 - Prealgebra

Question

Set up the following problems as you have been doing. Then use a calculator to perform the actual calculations. Round answers to two decimal places where appropriate. Lake Superior is the largest of the Great Lakes. It covers \(31,700\) square miles of area. What is the area of Lake Superior in acres?

Step-by-Step Solution

Answer

The area of Lake Superior is 20,288,000 acres.

Step 1: Understand the unit conversion

We need to convert from square miles to acres. There is a unit conversion factor between square miles and acres. Specifically, 1 square mile equals 640 acres.

Step 2: Set up the conversion

We start by writing the area of Lake Superior in square miles: 31,700 square miles. We will multiply this by the conversion factor to get the area in acres.

Step 3: Perform the calculation

Using the conversion factor, multiply the area in square miles by 640 to convert to acres: \[ 31,700 \text{ square miles} \times 640 \text{ acres/square mile} = 20,288,000 \text{ acres} \]

Step 4: Round the result

Since the problem does not specify further conditions for rounding acres, we take the calculated area. 20,288,000 is already an integer, and no further rounding for decimal places is needed.

Key Concepts

Area Conversion

When dealing with areas in different units, it's essential to understand how to convert between them, which is known as area conversion. Area conversion is similar to converting measurements like length or volume, but it involves units of squares. For example, square meters to square feet or, our focus here, square miles to acres. While each conversion has a specific factor or equation, the process generally involves multiplying by a conversion factor. Knowing these conversion factors, like 1 square mile equals 640 acres, helps in solving practical problems like understanding land areas in different units. It's a valuable skill as you might encounter one unit more frequently in certain contexts, and need to convert it to another to make comparisons or calculations more intuitive.

Square Miles to Acres

Square miles and acres are units used to measure large land areas, with square miles being larger than acres. For instance, when we discuss the size of large geographic regions like the Great Lakes, we often use square miles. Conversely, for farms or plots of land, acres might be more common. The conversion factor between these two is straightforward. One square mile equals 640 acres.

• This means if you have an area of 1 square mile, it covers 640 acres.
• To convert from square miles to acres, multiply the number of square miles by 640.
• This conversion helps track the size of enormous areas in smaller, more manageable units.

By using this conversion factor, you can quickly and easily understand the extent of very large areas, whether for homework problems or real-life applications.

Calculation Steps

Let's talk through the steps of performing a conversion from square miles to acres. Having a structured approach simplifies problem solving and ensures accuracy.First, identify the area you want to convert. In our example, this is Lake Superior's area: 31,700 square miles. Next, set up your calculation with the conversion factor. Multiply the square miles by the factor, 640 in this case, since that's how many acres are in one square mile:\[ 31,700 \text{ square miles} \times 640 \text{ acres/square mile} \]This calculation will give you an exact conversion of 20,288,000 acres. This large number can be hard to relate to intuitively, but knowing it covers many plots of typical land size can help.Always remember to consider rounding, but in this case, our final number did not have decimals, thus no rounding was necessary. Rounding usually helps in simplifying numbers to make them easier to read, especially when calculations end with long strings of decimals.