Converting units of measurement is a fundamental skill in many fields, from everyday tasks like cooking to complex scientific calculations. This article provides a detailed explanation of how to convert 87 centimeters (cm) to inches (in), exploring the underlying principles and offering various methods for solving similar conversion problems. We will move beyond simply providing the answer and delve into the "why" behind the conversion process, making it easier for students to grasp and apply these concepts in different contexts.
Understanding the Metric and Imperial Systems:
Before we begin the conversion, it's crucial to understand the two systems involved: the metric system and the imperial system.
Metric System (SI Units): This system, based on powers of 10, is the most widely used system globally. It uses units like meters (m) for length, grams (g) for mass, and liters (l) for volume. Centimeters (cm) are a subunit of the meter, with 100 centimeters equaling one meter (1 m = 100 cm).
Imperial System (US Customary Units): This system is primarily used in the United States and a few other countries. It utilizes units like inches (in), feet (ft), yards (yd), and miles (mi) for length, pounds (lb) for weight, and gallons (gal) for volume. The relationships between these units are not based on a simple power of 10, making conversions slightly more complex.
The Conversion Factor: The Bridge Between Systems
The key to converting between the metric and imperial systems lies in understanding the conversion factor. This factor represents the ratio between the two units. For length, the fundamental relationship is approximately:
1 inch (in) ≈ 2.54 centimeters (cm)
This means that one inch is equal to 2.54 centimeters. This is not an exact equivalence but a commonly used approximation sufficient for most purposes. More precisely, 1 in = 2.54 cm is defined.
Method 1: Direct Conversion using the Conversion Factor
To convert 87 cm to inches, we can use the conversion factor directly:
1. Set up the conversion: We want to go from centimeters to inches. We can write this as a fraction: (x inches) / (87 cm)
2. Apply the conversion factor: We know that 1 inch ≈ 2.54 cm. We can use this to create a ratio that cancels out the cm units:
(x inches) / (87 cm) = (1 inch) / (2.54 cm)
3. Solve for x: To isolate x (the number of inches), we multiply both sides of the equation by 87 cm:
x inches = (87 cm) (1 inch / 2.54 cm)
4. Calculate the result: The cm units cancel out, leaving:
x inches ≈ 34.25 inches
Therefore, 87 cm is approximately equal to 34.25 inches.
Method 2: Using Dimensional Analysis
Dimensional analysis is a powerful technique for ensuring accurate unit conversions. It involves systematically tracking the units throughout the calculation to ensure they cancel correctly. Let's apply this to our conversion:
87 cm (1 in / 2.54 cm) = 34.25 in
Notice how the "cm" units cancel, leaving only "in," confirming the correctness of our approach.
Method 3: Using Online Converters and Calculators
Numerous online converters and calculators are readily available to perform unit conversions. Simply enter the value in centimeters (87 cm in this case), select "centimeters" as the input unit, and "inches" as the output unit. These tools offer a quick and convenient method, but understanding the underlying principles (as explained above) remains crucial for solving more complex problems.
Significant Figures and Rounding:
When performing calculations involving measurements, it's essential to consider significant figures. The number 87 cm implies two significant figures. Our result of 34.25 inches should be rounded appropriately. Since 87 cm has two significant figures, we round our answer to two significant figures as well, resulting in 34 inches. However, for more precise calculations, retaining more decimal places might be necessary.
Practical Applications:
Understanding unit conversion is essential in many practical situations:
Sewing and Tailoring: Converting fabric measurements between centimeters and inches is crucial for accurate pattern making and garment construction.
Construction and Engineering: Converting measurements ensures precise construction and design in both metric and imperial systems.
International Trade: Accurate unit conversions are necessary for global commerce to ensure consistent product specifications.
Scientific Research: Converting units is essential for consistent data reporting and analysis across different research fields.
Summary:
Converting 87 centimeters to inches involves utilizing the conversion factor of approximately 1 inch = 2.54 centimeters. This conversion can be performed using direct calculation, dimensional analysis, or online converters. Understanding the metric and imperial systems and the concept of significant figures is crucial for accurate conversions. The ability to perform these conversions is essential across various fields, highlighting the importance of mastering this fundamental skill.
FAQs:
1. Is the conversion factor 1 inch = 2.54 cm exact? While often used as an approximation, 1 in = 2.54 cm is, in fact, an exact definition.
2. How do I convert inches back to centimeters? Simply reverse the process. Multiply the number of inches by 2.54 to get the equivalent in centimeters.
3. Why are there two different systems of measurement? The metric and imperial systems developed independently over time, leading to their continued use despite efforts towards global metrication.
4. What are some other common unit conversions involving length? Other common conversions include meters to feet, kilometers to miles, and millimeters to inches.
5. What happens if I use a different conversion factor? Using a different conversion factor will result in a different answer. It's crucial to use the standard and agreed-upon conversion factor (1 inch ≈ 2.54 cm) for consistency and accuracy.
Note: Conversion is based on the latest values and formulas.
Formatted Text:
80l to gallons 700 grams to lbs 360km to miles 260 pounds in kilos 148g to oz 160mm to inch 7325 in cm 38c to f 5000kg to lbs how many seconds are in 6 hours 16km in miles mortgage payment on 260k 40 miles to km 970 grams to pounds how much is 40000 a year per hour
