Perform each conversion. (a) \(22.5 \mathrm{in}\). to centimeters (b) \(126 \mathrm{ft}\) to meters (c) \(825 \mathrm{yd}\) to kilometers (d) \(2.4\) in. to millimeters

Understanding how to convert inches to centimeters is a fundamental skill in many fields, including engineering, construction, and everyday life. To make this conversion, you simply use the conversion factor that 1 inch equals 2.54 centimeters. This conversion factor is an exact value and is the basis for the conversion.

For a practical example, let's look at the textbook exercise where we need to convert 22.5 inches to centimeters. Using the conversion factor, you would multiply 22.5 (the number of inches) by 2.54 (the number of centimeters per inch). This results in a conversion calculation of: \( 22.5 \times 2.54 = 57.15 \), which means that 22.5 inches is equivalent to 57.15 centimeters.

When performing this calculation, it's helpful to use a calculator to ensure accuracy. Additionally, some common inch measurements and their corresponding centimeter conversions could be memorized for quicker reference, such as 1 inch (2.54 cm), 6 inches (15.24 cm), or 12 inches (30.48 cm).

When converting from feet to meters, the key is to use the correct conversion factor. One foot is officially defined as exactly 0.3048 meters. This precise factor is used globally to ensure consistency in measurements.

Let's apply this to the textbook problem where we have 126 feet that we want to convert to meters. You would carry out the calculation as such: \( 126 \times 0.3048 = 38.4048 \), which implies that 126 feet is equal to 38.4048 meters.

For quick reference and estimation, keeping in mind that a meter is roughly equal to 3 feet 3 inches can be handy, knowing that precise calculations always require the exact factor of 0.3048 meters per foot. This understanding is particularly useful in numerous applications, including athletics, real estate, and construction.

Yards to kilometers conversion may seem less common, but it is just as important, especially in fields like track and field or aviation where larger distances are frequently measured in yards or kilometers. The conversion process involves two steps, first converting yards to meters and then meters to kilometers.

One yard equals 0.9144 meters, and there are 1,000 meters in a kilometer. The textbook exercise provided asks us to convert 825 yards to kilometers. The initial step is to convert yards to meters: \( 825 \times 0.9144 = 754.38 \). Having converted the yards to meters, the next step is to convert meters to kilometers: \( 754.38 \div 1000 = 0.75438 \). Therefore, 825 yards is equivalent to 0.75438 kilometers.

It's crucial to remember that for longer distances, kilometers are more appropriate than meters, which is why this conversion can be particularly useful. Knowing how to convert between these units is essential for clear communication and understanding in contexts such as international sporting events or comparing distances between countries that may use different units of measurement.

Converting inches to millimeters is a common task in fields like engineering and manufacturing where precise measurements are critical. Since both inches and millimeters are used to measure smaller distances or lengths, it is important to understand how to convert between these units accurately. The conversion involves a two-step process, first converting inches to centimeters and then centimeters to millimeters.

To get the number of millimeters from inches, you first multiply the number of inches by 2.54 to get centimeters, because 1 inch is equivalent to 2.54 centimeters. Then you multiply the resultant centimeter value by 10, because 1 centimeter equals 10 millimeters. For example, in the textbook exercise, to convert 2.4 inches to millimeters, first convert inches to centimeters: \(2.4 \times 2.54 = 6.096 \), and then convert centimeters to millimeters: \(6.096 \times 10 = 60.96 \). Hence, 2.4 inches is equal to 60.96 millimeters.

Remember that for extremely precise measurements, especially in science and engineering projects, using millimeters is often more convenient than inches due to the metric system's base-10 structure, which simplifies calculations and conversions.