Problem 63 - 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. Death Valley National Monument contains \(2,067,795\) acres of land. How many square miles is this?

Step-by-Step Solution

Answer

Death Valley National Monument is approximately 3,230.93 square miles.

Step 1: Understanding the Conversion Factor

To convert acres to square miles, we need to know the conversion factor between these two units. There are 640 acres in one square mile. This is a standard unit conversion factor to keep in mind.

Step 2: Setting Up the Conversion

To convert from acres to square miles, divide the number of acres by the conversion factor. The formula to use is: \[ \text{square miles} = \frac{\text{acres}}{640} \]

Step 3: Applying the Formula

Substitute the given number of acres into the formula. We have 2,067,795 acres, so the calculation will be: \[ \text{square miles} = \frac{2,067,795}{640} \]

Step 4: Calculating the Result

Use a calculator to compute the division: \[ \text{square miles} = \frac{2,067,795}{640} \approx 3,230.93 \]

Step 5: Rounding the Answer

As the problem states, round the answer to two decimal places if necessary. In this case, the division already gives us \(3,230.93\) square miles, which is already rounded to two decimal places.

Key Concepts

Acres to Square Miles Conversion

Understanding how to convert acres to square miles is important when dealing with land measurement. Acres and square miles are both units of area used primarily in the United States to measure large pieces of land. However, given their different scales, they are used in different contexts.
To convert acres to square miles, start with the knowledge that there are precisely 640 acres in one square mile. This means that one square mile comprises a block of land that, if it were to be transformed into acres, would equal 640 separate, smaller pieces of land, each equivalent to one acre.

Conversion Factor

The conversion factor is a multiplier used when converting between different units of measurement. For acres to square miles, our conversion factor is 640.
Understanding this conversion factor is crucial because:

• It defines the relationship between the two units.
• Allows accurate and consistent conversions across various situations.
• Simplifies calculations when changing measurements from one unit to another.

By dividing the total number of acres by the conversion factor of 640, you directly convert the land measurement from acres into square miles, providing a larger unit which is often easier to comprehend for vast areas.

Rounding Decimal Places

Rounding to decimal places helps in representing numbers in a simpler and more manageable form. It is especially useful when dealing with large figures or precise computations.
In our example, we calculated the number of square miles to be approximately 3,230.93. Since the problem asks us to round to two decimal places, we've already arrived at the required precision. Here's why rounding is important:

• It makes numbers easier to read and understand.
• Ensures clarity in communication and documentation.
• Prevents confusion that can arise from overly detailed figures.

When rounding a number, you look to the third decimal place to decide whether the second decimal place stays the same or rounds up. In this case, the third decimal is insignificant, leaving the conversion smoothly rounded to 3,230.93.