Question

At the mall, you decide to try on a pair of French jeans. Naturally, the waist size of the jeans is given in centimeters. What does a waist measurement of \(52 \mathrm{cm}\) correspond to in inches?

Short answer

A waist measurement of 52 centimeters corresponds to approximately \(20.47 \, inches\).

Step-by-step solution

Identify the given measurement

We are given a waist measurement of 52 centimeters, which we need to convert to inches.

Apply the conversion factor

In order to convert a measurement from centimeters to inches, we need to use the conversion factor: 1 inch = 2.54 centimeters. So, we will divide the given measurement (52 cm) by 2.54.

Calculate the waist measurement in inches

Now, we will divide 52 centimeters by 2.54 to find the waist measurement in inches. \(waist\_in\_inches = \frac{52 \, cm}{2.54 \, cm/inch}\)

Simplify the expression

Upon simplifying the expression, we get: \(waist\_in\_inches = \frac{52}{2.54}\)

Find the value

Now, divide 52 by 2.54, and we get: \(waist\_in\_inches \approx 20.47 \, inches\) So, a waist measurement of 52 centimeters corresponds to approximately 20.47 inches.

Key concepts

Measurement Conversion in Chemistry

Measurement conversion is a vital skill in chemistry, where the need to understand and interchange between different units of measurement is crucial. It involves the process of changing one unit of measure to another without altering the quantity.

In the context of our exercise, converting a waist measurement from centimeters to inches, it's important to note that units of length are one of the most common conversions. This conversion hinges on knowing the correct unit factor, which for centimeters to inches is that one inch equals 2.54 centimeters. The process is straightforward: you divide the number of centimeters by 2.54 to get the equivalent in inches.

Understanding how to convert measurements allows for clearer communication and precision in both everyday life and scientific enterprises. Always stay aware of the units you are working with; in science, using the wrong unit can greatly affect the results of your work.

Metric to Imperial Conversion

Metric to imperial conversion is the transformation of units from the metric system (centimeters, meters, kilometers, etc.) to the imperial system (inches, feet, yards, miles, etc.), or vice versa. This is commonly used in many fields including science, construction, and even everyday shopping, as seen in our jeans sizing scenario.

In the United States, the imperial system is often used, making it necessary for many to understand how to convert to and from the metric system. To go from metric to imperial, you often need to divide by or multiply with a conversion factor. For length, as with our 52 centimeter waist measurement, you divide by 2.54 to convert to inches.

Remember that while some conversions are straightforward, others may require more complex factors. Use conversion tables or tools to assist you if needed. However, for common conversions involving length, volume, or mass between metric and imperial systems, memorizing key factors, such as 2.54 centimeters per inch, can be particularly useful.

Dimensional Analysis

Dimensional analysis, sometimes called the unit factor method or factor-label method, is a powerful tool for converting between units of measurement. It involves using conversion factors that express the equivalence between different units, and allows one to methodically follow units through calculations to ensure that the final result has the desired units.

For instance, when converting the 52 cm measurement to inches, dimensional analysis involves writing out the equation with units included and ensuring that units cancel out to leave only the desired result. Here, centimeters cancel out, and inches remain as follows:

Dimensional Analysis of Waist Measurement

\[\begin{equation}waist\_in\_inches = \frac{52 \, cm}{2.54 \, cm/inch}\end{equation}\]
As units are an integral part of the measurement, including them in calculations can prevent many common errors. Whether you're a student solving homework problems, or a professional scientist conducting experiments, mastering dimensional analysis is essential for accurate measurements.