Decoding the Metric System: Converting 164cm to Feet and Inches
The ability to convert between different units of measurement is a fundamental skill, particularly in a globalized world. While the metric system (using meters, centimeters, etc.) is prevalent internationally, the imperial system (using feet, inches, etc.) remains common in several countries. Therefore, understanding how to convert between these systems is crucial for various applications, from everyday tasks like understanding clothing sizes to more complex engineering projects. This article focuses specifically on converting 164 centimeters (cm) into feet and inches, breaking down the process step-by-step and explaining the underlying mathematical principles.
Understanding the Units:
Before we begin the conversion, it's important to establish the relationships between the units involved:
Centimeters (cm): A unit of length in the metric system. 100 centimeters equal 1 meter.
Meters (m): The base unit of length in the metric system.
Inches (in): A unit of length in the imperial system. 12 inches equal 1 foot.
Feet (ft): A unit of length in the imperial system.
The key to the conversion lies in knowing the conversion factor between the metric and imperial systems. A commonly used conversion factor is that 1 inch is approximately equal to 2.54 centimeters. This approximation is sufficient for most everyday conversions. For higher precision, more decimal places can be used.
Step-by-Step Conversion: 164cm to Feet and Inches
Our goal is to convert 164 cm into feet and inches. We will do this in two stages:
Stage 1: Converting Centimeters to Inches
Since 1 inch ≈ 2.54 cm, we can set up a proportion to find the equivalent number of inches:
(1 inch / 2.54 cm) = (x inches / 164 cm)
To solve for 'x' (the number of inches), we cross-multiply:
1 inch 164 cm = 2.54 cm x inches
164 inch-cm = 2.54 cm x inches
Now, we divide both sides by 2.54 cm:
x inches = 164 inch-cm / 2.54 cm
x inches ≈ 64.567 inches
The 'cm' units cancel out, leaving us with the number of inches. Note that we have a decimal value here – we'll handle this in the next step.
Stage 2: Converting Inches to Feet and Inches
We now have approximately 64.567 inches. To express this in feet and inches, we need to determine how many full feet are present and the remaining inches.
Since 1 foot = 12 inches, we divide the total inches by 12:
64.567 inches / 12 inches/foot ≈ 5.38 feet
This tells us that there are approximately 5 full feet. To find the remaining inches, we look at the decimal part of the result (0.38 feet). We multiply this decimal by 12 inches/foot:
0.38 feet 12 inches/foot ≈ 4.56 inches
Therefore, 164 cm is approximately equal to 5 feet and 4.56 inches. We can round this to 5 feet and 4.6 inches for practical purposes.
Mathematical Concepts Used:
This conversion relies on several key mathematical concepts:
Proportions: We used a proportion to relate the known conversion factor (1 inch ≈ 2.54 cm) to the unknown value (x inches). Proportions are a fundamental tool for solving problems involving ratios and scales.
Unit Conversion: This involves multiplying or dividing by conversion factors to change units while preserving the value of the quantity. This is crucial in many scientific and engineering applications.
Division and Multiplication: These basic arithmetic operations were used throughout the calculation to solve for the unknown variables and express the result in the desired units.
Rounding: Since we used an approximation for the conversion factor and obtained decimal values, we rounded the final answer to a reasonable level of precision. This reflects the inherent limitations in using approximate values.
Summary:
Converting 164 cm to feet and inches involves a two-step process: first converting centimeters to inches using the conversion factor 1 inch ≈ 2.54 cm, and then converting inches to feet and inches by dividing by 12 inches/foot. This process highlights the importance of understanding unit conversions and utilizing basic mathematical operations like proportions and division. The final result, using a commonly used approximation, is approximately 5 feet and 4.6 inches.
Frequently Asked Questions (FAQs):
1. Why is the conversion not exact? The conversion is not exact because the conversion factor 1 inch ≈ 2.54 cm is an approximation. The exact conversion factor involves more decimal places.
2. Can I use a different conversion factor? Yes, you can use a more precise conversion factor (e.g., 1 inch = 2.540005 cm) for increased accuracy, but for most purposes, 2.54 cm is sufficient.
3. What if I want to convert feet and inches back to centimeters? To convert from feet and inches to centimeters, reverse the process. First, convert feet to inches (multiply by 12), then add the remaining inches. Finally, convert the total inches to centimeters (multiply by 2.54).
4. Are there online calculators for this conversion? Yes, many online calculators are readily available to perform unit conversions, including centimeters to feet and inches. These can be a helpful tool for quick conversions.
5. Is there a single formula to perform this conversion? While there isn't a single, compact formula, the process can be summarized as: `(cm / 2.54) / 12 = feet` and the remainder, when multiplying the decimal part by 12, gives the remaining inches. This shows the two-step nature of the conversion.
Note: Conversion is based on the latest values and formulas.
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