Problem 43 - 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. Sewing 25 square yards of material is how many square meters?

Step-by-Step Solution

Answer

25 square yards is approximately 20.90 square meters.

Step 1: Understanding the Problem

We need to convert 25 square yards into square meters. This involves using the conversion factor between square yards and square meters.

Step 2: Conversion Factor Identification

Identify the conversion factor: 1 square yard equals approximately 0.836127 square meters.

Step 3: Setting Up the Conversion

Multiply the number of square yards by the conversion factor to convert it to square meters. The expression is: \[ 25 \text{ square yards} \times 0.836127 \text{ square meters/square yard} \]

Step 4: Perform the Calculation

Use a calculator to compute the product. Multiply 25 by 0.836127 to get the area in square meters.

Step 5: Rounding to the Nearest Hundredth

Round the calculated value to the nearest hundredth. The calculator gives us approximately 20.903175 square meters, which is rounded to 20.90 square meters.

Key Concepts

Conversion Factor

When converting from one unit of measurement to another, a conversion factor is necessary. It acts as a bridge between the two units, allowing for accurate conversions. In unit conversion, the conversion factor is a ratio that expresses how many of one unit is equivalent to another. For example:

• The conversion factor between square yards and square meters is approximately 0.836127.

Using this factor, you can convert any given area from square yards to square meters, or vice versa. To convert a quantity, multiply it by the conversion factor. In our problem, we multiply 25 square yards by the conversion factor 0.836127 to determine the equivalent area in square meters. This ensures that unit conversions are precise and help in making proper measurements.

Area Measurement

Area measurement is a way to quantify the surface area of a two-dimensional shape or space. It's essential in numerous fields like construction, sewing, and interior design.

• Square yards and square meters are common units of area measurement.
• One square yard refers to a square with sides of one yard long.
• One square meter refers to a square with sides of one meter long.

Understanding how to measure and convert these units of area is crucial in ensuring accuracy and efficiency in various tasks. For the conversion problem at hand, we need to calculate how many square meters correspond to 25 square yards. This is done using the appropriate conversion factor, ensuring all measurements and results are accurate and relevant for the task at hand.

Rounding Decimals

Rounding decimals is an essential mathematical operation, especially in real-world applications, where absolute precision might not be necessary or possible. It helps simplify numbers, making them easier to read and work with. When rounding to the nearest hundredth, you focus on the second digit after the decimal point.

• If the third digit is five or greater, you round up the second digit.
• If the third digit is less than five, you leave the second digit unchanged.

In the exercise, after multiplying 25 square yards by 0.836127, the calculator gives an answer of approximately 20.903175 square meters. To simplify and present this value clearly, it is rounded to 20.90 square meters. This level of precision is typically sufficient for practical purposes, providing a balance between accuracy and simplicity.