Question

Perform the following conversions. (a) \(2.4 \mathrm{yd}^{2}\) to \(\mathrm{m}^{2}\) (c) \(9.1 \mathrm{ft}^{3}\) to \(\mathrm{L}\) (b) \(8.3 \mathrm{in} .^{2}\) to \(\mathrm{mm}^{2}\)

Short answer

a) 2.4 yd^2 = 2.006705 m^2, c) 9.1 ft^3 = 257.6828 L, b) 8.3 in^2 = 5356.828 mm^2.

Step-by-step solution

Convert Square Yards to Square Meters

To convert square yards to square meters, you can use the conversion factor that 1 square yard is equal to approximately 0.836127 square meters. Multiply the area in square yards by the conversion factor: 2.4 yd^2 * 0.836127 m^2/yd^2.

Calculate the Conversion for Square Yards to Square Meters

Perform the multiplication to find the area in square meters: 2.4 * 0.836127 m^2/yd^2 = 2.006705 m^2.

Convert Cubic Feet to Liters

For converting cubic feet to liters, use the conversion factor that 1 cubic foot is equal to 28.3168 liters. Multiply the volume in cubic feet by the conversion factor: 9.1 ft^3 * 28.3168 L/ft^3.

Calculate the Conversion for Cubic Feet to Liters

Perform the multiplication to find the volume in liters: 9.1 ft^3 * 28.3168 L/ft^3 = 257.6828 L.

Convert Square Inches to Square Millimeters

To convert square inches to square millimeters, use the conversion factor that 1 square inch is equal to 645.16 square millimeters. Multiply the area in square inches by the conversion factor: 8.3 in^2 * 645.16 mm^2/in^2.

Calculate the Conversion for Square Inches to Square Millimeters

Carry out the multiplication to find the area in square millimeters: 8.3 in^2 * 645.16 mm^2/in^2 = 5356.828 mm^2.

Key concepts

Square Yards to Square Meters

Understanding unit conversion is essential in chemistry and many other fields, to accurately perform measurements in different units of area. To convert square yards to square meters, which are units of area, we need to know the conversion factor between the two. One square yard is approximately equal to 0.836127 square meters. To convert an area from square yards to square meters, you multiply the given value by this conversion factor.

For example, converting 2.4 square yards to square meters involves multiplying 2.4 by 0.836127, which is the conversion factor. The following mathematical process illustrates this:
\(2.4 \text{ yd}^2 \times 0.836127 \frac{\text{m}^2}{\text{yd}^2} = 2.006705 \text{ m}^2\).

It's important to ensure that your final answer is in squared units since we are dealing with areas. This conversion is widely used in various real-life applications, such as land measurement and flooring. It's also a fundamental concept in science classes, where problems often need to be understood and solved in a global context using the metric system.

Cubic Feet to Liters

Volume conversions are similar to area conversions but with a focus on three-dimensional space, which is particularly useful in chemistry when dealing with liquids and gases. When converting from cubic feet to liters, we use a different conversion factor because we are now considering volume. The conversion factor to remember here is that one cubic foot equals 28.3168 liters.

To convert 9.1 cubic feet to liters, you would multiply 9.1 by 28.3168. Here is the calculation in a clear format:
\(9.1 \text{ ft}^3 \times 28.3168 \frac{\text{L}}{\text{ft}^3} = 257.6828 \text{ L}\).

This conversion is crucial when you need to measure larger volumes, especially in areas such as brewing, aquarium sizing, and even in the automotive industry for engine displacement. In chemistry labs, measuring volumes of liquids precisely is crucial for experiment accuracy, making this conversion fundamental for students. The metric system is the standard in scientific measurement, so converting to liters aligns with global practices.

Square Inches to Square Millimeters

The conversion from square inches to square millimeters is often encountered in small-scale measurements, typically in fields such as material science and engineering. The conversion factor used for this transformation is that there are 645.16 square millimeters in a square inch.

To convert an area, say 8.3 square inches, to square millimeters, multiply the value in square inches by 645.16, the conversion factor:
\(8.3 \text{ in}^2 \times 645.16 \frac{\text{mm}^2}{\text{in}^2} = 5356.828 \text{ mm}^2\).

Ensuring precision in this conversion is valuable when working on detailed technical drawings, cutting materials to specific sizes, or manufacturing parts that require high precision. The conversion is straightforward but requires accuracy as small errors can lead to significant issues in these contexts. For students, mastering this type of conversion is vital for a deep understanding of scaling and measurements across different units and standards.