The Problem: The metric system, while logically consistent, can present challenges when converting between units. Imagine you're an online retailer selling handcrafted jewelry. You've meticulously crafted a necklace with a chain length of 48 centimeters. Your international customers, however, are more comfortable with inches or feet. How do you accurately convert 48 centimeters to these units, ensuring consistent and accurate product descriptions to avoid confusion and returns? This problem highlights a common need: the reliable conversion of 48 centimeters (cm) to other units of length. This article will provide a clear and comprehensive guide to solve this and similar problems.
Step-by-Step Solutions & Strategies:
Converting 48 centimeters involves understanding the fundamental relationships between centimeters, inches, feet, and other units of length. The key to successful conversion is using conversion factors.
Solution 1: Converting Centimeters to Inches:
One inch is approximately equal to 2.54 centimeters. This is the fundamental conversion factor we will use.
Step 1: Identify the conversion factor.
Our conversion factor is 1 inch = 2.54 cm.
Step 2: Set up the conversion equation.
To convert 48 cm to inches, we set up a proportion:
```
x inches / 48 cm = 1 inch / 2.54 cm
```
Where 'x' represents the number of inches.
Step 3: Solve for x.
To solve for 'x', we cross-multiply:
```
x inches 2.54 cm = 48 cm 1 inch
```
Then, divide both sides by 2.54 cm:
```
x inches = (48 cm 1 inch) / 2.54 cm
```
The 'cm' units cancel out, leaving:
```
x inches ≈ 18.9 inches
```
Therefore, 48 centimeters is approximately 18.9 inches.
Real-world example: Returning to our jewelry example, the product description for the necklace should accurately state that the chain length is approximately 18.9 inches. This clarifies the length for international customers accustomed to the imperial system.
Solution 2: Converting Centimeters to Feet:
Since there are 12 inches in a foot, we can build upon our previous conversion.
Step 1: Convert centimeters to inches (as shown in Solution 1). We already know that 48 cm is approximately 18.9 inches.
Step 2: Convert inches to feet.
The conversion factor is 1 foot = 12 inches. We set up the proportion:
```
x feet / 18.9 inches = 1 foot / 12 inches
```
Step 3: Solve for x.
Cross-multiply and solve:
```
x feet = (18.9 inches 1 foot) / 12 inches
```
The 'inches' units cancel out:
```
x feet ≈ 1.575 feet
```
Therefore, 48 centimeters is approximately 1.575 feet.
Real-world Example: A carpenter needs a piece of wood 48 centimeters long for a project. Knowing that this is approximately 1.575 feet allows for accurate measurement using a standard measuring tape calibrated in feet and inches.
Solution 3: Using Online Converters:
Numerous online converters are readily available. Simply search for "centimeter to inch converter" or "centimeter to feet converter" and input the value 48. These tools often provide multiple unit conversions simultaneously, offering a quick and easy solution. However, it's crucial to understand the underlying principles to ensure accurate results and avoid misinterpretations.
Summary:
Converting 48 centimeters to other units of length involves utilizing conversion factors and setting up proportions. The key conversion factor is 1 inch = 2.54 cm. We can use this to convert to inches and then to feet. Online converters offer a convenient alternative, but understanding the fundamental principles is crucial for accurate and reliable results in various applications. Accurate conversion ensures clear communication and avoids potential errors in diverse fields, ranging from crafting and construction to international commerce and scientific measurements.
Frequently Asked Questions (FAQs):
1. Are the conversions exact? No, the conversions are approximate because the conversion factor (1 inch = 2.54 cm) is a rounded value. More precise conversions might involve more decimal places.
2. How do I convert centimeters to other units like meters or kilometers? The metric system is based on powers of 10, simplifying conversions. 1 meter = 100 centimeters, and 1 kilometer = 1000 meters. Therefore, 48 cm = 0.48 meters and 0.00048 kilometers.
3. What if I need to convert from inches or feet back to centimeters? Simply reverse the process. Use the conversion factors (1 inch = 2.54 cm and 1 foot = 12 inches) and set up a proportion to solve for centimeters.
4. Are there any potential sources of error in these conversions? Errors can arise from rounding off values during calculations or using inaccurate conversion factors. Using more significant figures in the conversion factor (e.g., 1 inch = 2.5400 centimeters) can increase accuracy.
5. Which method is best for quick conversions? Online converters are the fastest method for quick conversions, but understanding the manual calculation method is essential for verifying results and handling situations where an online converter isn't available.
Note: Conversion is based on the latest values and formulas.
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