This article provides a detailed explanation of how to convert centimeters (cm) to inches (in), using 142 cm as a practical example. We'll explore the underlying principles of unit conversion, demonstrate the calculation process, and delve into the practical applications of this conversion. This guide aims to equip students with a thorough understanding, beyond simply obtaining the answer.
1. Understanding Units of Measurement:
Before we begin the conversion, it's crucial to understand the fundamental units involved: centimeters and inches. Both are units of length, but they belong to different systems of measurement.
Centimeters (cm): Part of the metric system, a decimal system based on powers of 10. It's a common unit for measuring smaller lengths. One centimeter is one-hundredth of a meter (1 cm = 0.01 m). The metric system is used globally in science and is preferred in many countries.
Inches (in): Part of the imperial system, a system with less straightforward relationships between units. It's commonly used in the United States and a few other countries. One inch is a fractional part of a foot (1 in = 1/12 ft) and a yard (1 in = 1/36 yd).
The difference in the systems necessitates a conversion factor to move seamlessly between them.
2. The Conversion Factor:
The key to converting between centimeters and inches lies in the conversion factor. This factor represents the ratio between the two units. The established conversion factor is:
1 inch ≈ 2.54 centimeters
The "≈" symbol means "approximately equal to" because the conversion factor is a rounded value. More precise values exist, but 2.54 cm/in is sufficient for most practical applications.
3. Converting 142 cm to Inches: The Calculation
Now, let's apply this conversion factor to convert 142 cm to inches. We can use a simple proportion or a direct calculation:
a) Using Proportion:
We can set up a proportion:
1 in / 2.54 cm = x in / 142 cm
To solve for 'x' (the number of inches), we cross-multiply:
1 in 142 cm = 2.54 cm x in
142 in cm = 2.54 cm x in
Divide both sides by 2.54 cm:
x in = 142 in cm / 2.54 cm
The 'cm' units cancel out, leaving:
x in ≈ 55.91 inches
b) Direct Calculation:
Alternatively, we can directly use the conversion factor:
142 cm (1 in / 2.54 cm) = 55.91 in
Again, the 'cm' units cancel out, leaving the answer in inches.
4. Understanding Significant Figures:
The precision of our answer is dictated by the significant figures in the original measurement and the conversion factor. Our initial value, 142 cm, has three significant figures. The conversion factor (2.54 cm/in) is considered to have an unlimited number of significant figures in this context because it's a defined value. Therefore, our final answer, 55.91 inches, should ideally be rounded to three significant figures, resulting in 55.9 inches.
5. Practical Applications:
Converting between centimeters and inches is crucial in various fields:
Engineering and Manufacturing: Designing products that need to meet specifications from different countries requires seamless unit conversion.
Construction: Converting blueprints or measurements from one system to another.
Textiles and Clothing: Sizing garments often involves conversions between the metric and imperial systems.
Science and Research: Reporting measurements consistently across different contexts.
6. Working with Other Units:
The same principle of using conversion factors applies to converting centimeters to other units of length, such as meters, kilometers, feet, yards, or miles. For instance, to convert centimeters to meters, we would use the factor 1 meter = 100 centimeters.
Summary:
Converting 142 centimeters to inches involves utilizing the conversion factor of approximately 2.54 centimeters per inch. Through either proportion or direct calculation, we find that 142 cm is approximately equal to 55.9 inches. Understanding significant figures ensures the precision of our answer aligns with the input value. This conversion is vital in numerous fields requiring interoperability between the metric and imperial systems of measurement.
Frequently Asked Questions (FAQs):
1. Is the conversion factor 2.54 cm/in exact? No, it's a rounded value. The exact value is more complex, but 2.54 is accurate enough for most everyday conversions.
2. How do I convert inches back to centimeters? Simply reverse the process. Multiply the number of inches by 2.54 cm/in.
3. What if I have a measurement with fractions of an inch? Convert the fractional part of an inch to a decimal (e.g., 1/2 inch = 0.5 inches) before applying the conversion factor.
4. Can I use online converters? Yes, many online converters are available to perform this conversion quickly. However, understanding the underlying principles is important for problem-solving and avoiding errors.
5. Why are there two different systems of measurement? The metric system emerged later and is based on a more logical and consistent decimal system. The imperial system developed over time, resulting in less straightforward relationships between units. While efforts are underway for global adoption of the metric system, both systems remain in use.
Note: Conversion is based on the latest values and formulas.
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