Problem 85 - Elementary Algebra

Question

A standard rectangular city block in Manhattan is about \(264 \mathrm{ft}\) by \(900 \mathrm{ft}\). One acre of land is \(43,560 \mathrm{ft}^{2}\). Find the size of a standard city block in acres. Round to the nearest tenth.

Step-by-Step Solution

Answer

5.5 acres

Step 1 - Find the area of the city block in square feet

Multiply the length and width of the city block to find its area. Area = length × width Area = 264 ft × 900 ft = 237,600 ft²

Step 2 - Convert the area from square feet to acres

Divide the area of the city block by the number of square feet in an acre to convert to acres. Number of acres = \(\frac{237,600 \text{ ft}²}{43,560 \text{ ft}²/\text{acre}}\) ≈ 5.5 acres

Step 3 - Round to the nearest tenth

Since we have already calculated that \(\frac{237,600 \text{ ft}²}{43,560 \text{ ft}²/\text{acre}} ≈ 5.5\), the value is already rounded to the nearest tenth.

Key Concepts

Rectangular Area Calculation

To find the area of a rectangular city block, you can use a simple formula: multiply the length of the block by its width. This is an important concept in algebra and geometry. For the given problem, the length of the city block is 264 feet and the width is 900 feet. To determine the area, you multiply these two values together:
Area = 264 ft × 900 ft = 237,600 ft².
This means the total surface area of the block is 237,600 square feet. Rectangular area calculation is widely used in many fields such as construction and land surveying, making it a fundamental skill in algebra.

Conversion between Units

When dealing with measurements, you often need to convert units. In this problem, you need to convert the area from square feet to acres. One acre is defined as 43,560 square feet. To convert the area of the city block into acres, you divide the block’s area by the number of square feet in an acre:
Number of acres = \(\frac{237,600 \text{ ft}²}{43,560 \text{ ft}²/\text{acre}}\)
Performing this division gives:
Number of acres ≈ 5.5 acres.
Converting between units is crucial in many scientific and engineering fields to ensure precision and understanding across different measurement systems.

Mathematical Rounding

Rounding numbers helps to simplify results and make them easier to understand. In this exercise, you round the number of acres to the nearest tenth. The value calculated from division was already close to a simple number: 5.5. When rounding to the nearest tenth, you look at the digit in the hundredths place. If it is 5 or more, you round the digit in the tenths place up by one. In this case, since the calculated value was exactly 5.5, it remains rounded to 5.5 acres.
Rounding is a common mathematical practice employed in everyday calculations to maintain simplicity and readability.