147cm to ft Convert: A Comprehensive Guide for Students
Converting units of measurement is a fundamental skill in many scientific and practical fields. Understanding the process not only helps in solving problems but also strengthens your grasp of fundamental mathematical concepts. This article delves into the conversion of 147 centimeters (cm) to feet (ft), exploring the underlying principles and providing a step-by-step approach suitable for students of all levels.
1. Understanding Units of Measurement:
Before we begin the conversion, it's crucial to understand the units involved. Centimeters (cm) are a unit of length in the metric system, based on powers of ten. One centimeter is one-hundredth of a meter (1 cm = 0.01 m). Feet (ft), on the other hand, are a unit of length in the imperial system, a system with less consistent relationships between its units. The imperial system's complexity often makes conversions more challenging than those within the metric system.
2. The Conversion Factor:
The key to converting between centimeters and feet lies in understanding their relationship. This relationship is represented by a conversion factor. We know that 1 inch (in) is equal to 2.54 centimeters (cm). Since 1 foot (ft) contains 12 inches, we can derive the conversion factor between centimeters and feet:
1 ft = 12 in = 12 in (2.54 cm/in) = 30.48 cm
Therefore, 1 foot is equal to 30.48 centimeters. This is our crucial conversion factor. This allows us to create a ratio that we can use to convert from one unit to the other.
3. Converting 147 cm to ft: The Calculation
Now that we have our conversion factor, we can convert 147 cm to feet. We can set up a proportion or use dimensional analysis.
Method 1: Proportion
We can set up a proportion using the conversion factor:
1 ft / 30.48 cm = x ft / 147 cm
To solve for x (the number of feet), we cross-multiply:
1 ft 147 cm = 30.48 cm x ft
147 cm-ft = 30.48 cm x ft
Divide both sides by 30.48 cm:
x ft = 147 cm-ft / 30.48 cm
x ≈ 4.82 ft
Method 2: Dimensional Analysis
Dimensional analysis is a powerful technique that uses conversion factors to cancel out units. We start with the given value (147 cm) and multiply by the conversion factor:
147 cm (1 ft / 30.48 cm) = 4.82 ft (approximately)
Notice how the "cm" units cancel out, leaving us with the desired unit, "ft". This method ensures that we are correctly applying the conversion factor and that the units are consistent.
4. Understanding Significant Figures:
The precision of our answer is limited by the precision of our measurements and conversion factors. The value 30.48 cm/ft is a defined conversion, so it has infinite significant figures. However, 147 cm likely has only three significant figures. Therefore, our answer of 4.82 ft should also be expressed with three significant figures. Rounding to fewer significant figures would introduce unnecessary error.
5. Practical Applications:
Converting between centimeters and feet has numerous practical applications. For example:
Construction and Engineering: Converting blueprint measurements from metric to imperial units.
Interior Design: Adapting furniture dimensions for different countries or regions.
Sports: Converting athletic performance statistics (e.g., high jump results).
International Trade: Ensuring compatibility of products with different measurement standards.
Summary:
Converting 147 cm to feet involves understanding the relationship between the two units and utilizing a conversion factor. We determined that 1 foot is equal to 30.48 centimeters. Using this factor, either through proportion or dimensional analysis, we found that 147 cm is approximately equal to 4.82 feet. The precision of the result is governed by the significant figures of the input value. Understanding these concepts is crucial for accurate conversions and problem-solving across various disciplines.
Frequently Asked Questions (FAQs):
1. Why is the conversion factor 30.48 cm/ft? This factor is derived from the established relationship between inches and centimeters (1 inch = 2.54 cm) and the fact that there are 12 inches in a foot.
2. Can I use an online converter instead of calculating manually? Yes, online converters are readily available and convenient, but understanding the underlying principles of conversion is crucial for deeper comprehension.
3. What if I need to convert feet to centimeters? You would simply reverse the conversion factor: multiply the number of feet by 30.48 cm/ft.
4. How do significant figures affect the accuracy of my answer? Significant figures represent the precision of a measurement. The result of a calculation should not be expressed with more significant figures than the least precise measurement involved.
5. Are there other ways to convert between centimeters and feet? While the method described is the most straightforward, other methods involving multiple conversion steps (e.g., cm to inches to feet) are possible, but generally less efficient.
Note: Conversion is based on the latest values and formulas.
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