Problem 37 - Chemistry: Principles and Reactions

Question

The unit of land measure in the English system is the acre, while that in the metric system is the hectare. An acre is \(4.356 \times 10^{4} \mathrm{ft}^{2} .\) A hectare is ten thousand square meters. The town of Willington in Connecticut requires a minimum area of \(2.0\) acres of land for a single-family dwelling. How many hectares are required?

Step-by-Step Solution

Answer

Answer: The minimum area required for a single-family dwelling in the town of Willington is approximately 0.80937 hectares.

Step 1: Convert acres to square feet

Given that 1 acre is equal to \(4.356 \times 10^4\) square feet, start by multiplying 2 acres by this conversion factor: 2 acres * \(4.356 \times 10^4 \mathrm{ft}^2\) per acre.

Step 2: Convert square feet to square meters

Now, we need to convert square feet to square meters using the conversion factor 1 square foot = 0.092903 square meters: \(2 \times 4.356 \times 10^4 \mathrm{ft}^2 \times 0.092903 \frac{\mathrm{m}^2}{\mathrm{ft}^2}\)

Step 3: Convert square meters to hectares

Finally, we'll convert square meters to hectares using the conversion factor 1 hectare = 10,000 square meters: \(\frac{2 \times 4.356 \times 10^4 \times 0.092903}{10000} \mathrm{hectares}\) Now, calculate the result: \(\frac{2 \times 4.356 \times 10^4 \times 0.092903}{10000} \approx 0.80937\) hectares Therefore, 2 acres is approximately 0.80937 hectares. So, the minimum area required for a single-family dwelling in the town of Willington is approximately 0.80937 hectares.

Key Concepts

Understanding Acre to Hectare Conversion

When dealing with land measurement, the conversion between different units is crucial for various practical applications, such as real estate transactions, urban planning, and agricultural management. An acre is a unit of area commonly used in the United States, wheras the hectare is a metric unit widely used internationally. To convert between these two, understanding the exact conversion factors is key.

One acre is equivalent to approximately 0.404686 hectares. Therefore, when you want to convert acres to hectares, you multiply the number of acres by this conversion factor. The provided exercise required the conversion of 2 acres to hectares, which involved multiplying 2 by 0.404686 to find the equivalent area in hectares. The resulting figure is important for those complying with local regulations, such as the minimum land area needed for housing, as demonstrated in the Willington example.

Navigating Through Area Measurement Units

In everyday and professional contexts, we deal with various units of area measurement. Commonly, we use square feet or square meters for smaller plots of land, and acres or hectares for larger areas. For instance, in the United States, you'll often encounter acres, while in many other countries, hectares are the standard.

It's useful to know that one acre is equivalent to exactly 43,560 square feet or about 4,047 square meters. Conversely, one hectare, which is equal to 10,000 square meters, is roughly 2.471 acres. Each unit is part of a bigger system – acres belong to the Imperial and US customary systems, while hectares are a part of the metric system. Understanding these relationships is fundamental for scientists, engineers, and land professionals, and is particularly useful for students to master for both academic purposes and real-world applications.

Mastering Metric System Conversion

The metric system is an internationally adopted system of units based on multiples of ten, making it straightforward to shift between units such as meters, liters, and grams. In the context of area measurement, square meters and hectares are the metric units most commonly used. To convert within the metric system, you often simply multiply or divide by powers of ten. For example, to convert square meters to hectares, you divide by 10,000, since one hectare is defined as 10,000 square meters.

Converting units within the metric system is a foundational skill in science and engineering fields. It also comes in handy in real-life situations, such as interpreting land size when traveling or purchasing property abroad. Mastering this skill enhances one's numeracy and global competence, as it translates directly to everyday tasks and is frequently employed in scientific research and international trade.