Problem 48 - Prealgebra

Question

Set up the following problems as we have set up the examples in this section. Then use a calculator for the calculations and round your answers to the nearest hundredth. Farming A farmer owns 57 acres of land. How many hectares is that?

Step-by-Step Solution

Answer

The farmer owns 23.07 hectares.

Step 1: Understand the Unit Conversion

To convert acres to hectares, we need to know that 1 acre equals approximately 0.404686 hectares. This is a fixed conversion factor used in area conversions between acres and hectares.

Step 2: Set Up the Conversion Equation

We know the farmer owns 57 acres. We can convert acres to hectares by multiplying the number of acres by the conversion factor from Step 1. Thus, the equation becomes:\[57 \text{ acres} \times 0.404686 \text{ hectares/acre}\]

Step 3: Perform the Calculation

Using a calculator, compute the result of the multiplication:\[57 \times 0.404686 = 23.0661\]

Step 4: Round to the Nearest Hundredth

The result from Step 3 is 23.0661 hectares. Rounding this to the nearest hundredth gives us 23.07 hectares.

Key Concepts

Area Conversions

Area conversions involve converting one unit of area measurement to another. This usually requires a specific conversion factor, which acts as a bridge between the two units. For instance, in this exercise, we needed to convert acres into hectares. Every unit has its own conversion factor, and for acres to hectares, the conversion factor is approximately 0.404686. This means that for every acre, you have a little over 0.4 hectares. To perform the conversion, multiply the number of acres by this conversion factor. This gives you the equivalent area in hectares.

• The conversion factor is fixed, meaning it doesn't change.
• Understanding conversion factors is key for accurate conversions.
• Multiply the number of original units by the conversion factor to find the number of new units.

This knowledge is not only essential for farming, as illustrated in the problem, but also for construction and real estate, where understanding land size in different units can be crucial.

Using a Calculator

When dealing with numbers that involve more than simple calculations, using a calculator can save time and ensure accuracy. Calculators can handle multiplications, like in this exercise, where 57 acres were multiplied by the conversion factor to compute hectares. By entering the exact values into a calculator, you reduce the risk of making errors that can occur with manual calculations.

• Ensure you're inputting the digits accurately, especially the conversion factor.
• Double-check the calculator's display before and after hitting enter to verify the result.
• Using a calculator is especially beneficial for complex calculations or large numbers.

Calculators can be digital or online, and many have memory functions to store values or results. With practice, it becomes easier to handle calculations quickly and accurately.

Rounding Decimals

Rounding decimals makes large or complex numbers easier to work with by reducing them to a specified number of decimal places. This exercise required rounding the result of 23.0661 hectares to the nearest hundredth, which is 23.07 hectares. Rounding to the nearest hundredth means keeping two digits to the right of the decimal point.

• If the third decimal digit is 5 or more, increase the second digit by one.
• If the third decimal digit is less than 5, leave the second digit as it is.
• Rounding helps in presenting clean, understandable results without impacting the overall value significantly.

This is a helpful practice in many fields such as finance, science, and engineering, where exact precision isn't always necessary for reporting or estimations.