The ability to convert units of measurement is a fundamental skill in mathematics and science. It's crucial for various applications, from everyday tasks like cooking (following recipes that use both metric and imperial units) to more complex engineering projects requiring precise calculations. This article will focus on a seemingly simple conversion: converting 90 centimeters (cm) into inches (in). While the conversion itself is straightforward, we'll explore the underlying mathematical concepts to provide a thorough understanding applicable to other unit conversions.
Understanding the Relationship Between Centimeters and Inches
The metric system (based on centimeters, meters, kilometers, etc.) and the imperial system (based on inches, feet, yards, etc.) are two distinct systems of measurement. They don't share a simple, whole-number relationship; instead, they rely on a conversion factor. This factor represents the ratio between the two units. In this case, the conversion factor between centimeters and inches is approximately 2.54 centimeters per inch. This means that 1 inch is equal to 2.54 centimeters.
Step-by-Step Conversion: 90 cm to Inches
We'll approach this conversion using two methods: a direct calculation using the conversion factor and a dimensional analysis approach, which emphasizes the cancellation of units.
Method 1: Direct Calculation
1. Identify the conversion factor: We know that 1 inch = 2.54 centimeters. This can be written as a fraction: 1 in / 2.54 cm or 2.54 cm / 1 in.
2. Choose the correct fraction: Since we want to convert centimeters to inches, we need the fraction that will cancel out the centimeters unit and leave us with inches. We choose the fraction 1 in / 2.54 cm.
3. Set up the equation: We multiply the given value (90 cm) by the chosen fraction:
90 cm (1 in / 2.54 cm)
4. Perform the calculation: Notice that the "cm" units cancel out:
(90 1 in) / 2.54 = 35.433 in (approximately)
Therefore, 90 centimeters is approximately equal to 35.433 inches.
Method 2: Dimensional Analysis
Dimensional analysis is a powerful technique that ensures we're using the correct units and performing the calculation correctly. It involves tracking the units throughout the process, allowing us to see how they cancel out and ensuring the final answer has the desired units.
1. Start with the given value and its units: 90 cm
2. Multiply by the conversion factor: We use the same conversion factor as in Method 1: (1 in / 2.54 cm). Note that this fraction is equivalent to 1, because 1 inch IS 2.54 cm. Multiplying by 1 doesn't change the value, only the units.
3. Set up the equation and cancel units:
90 cm (1 in / 2.54 cm)
The "cm" units cancel out:
90 (1 in) / 2.54
4. Perform the calculation:
90 / 2.54 ≈ 35.433 in
Again, we arrive at the same result: 90 centimeters is approximately 35.433 inches.
Understanding Significant Figures
The number of significant figures in a measurement reflects the precision of that measurement. Since our conversion factor (2.54 cm/in) is considered exact (by definition), the number of significant figures in our answer is determined by the given value (90 cm). 90 cm has two significant figures (we assume it is measured to the nearest 10 cm, not the nearest cm). Therefore, a more appropriate answer would be 35 inches, reflecting the lower precision of the original measurement. Using more decimal places implies a higher degree of accuracy than what the original measurement warrants.
Beyond 90 cm: Generalizing the Conversion
The methods described above can be easily applied to convert any number of centimeters to inches. Simply substitute the given number of centimeters for 90 in the equations.
For example, to convert 150 cm to inches:
150 cm (1 in / 2.54 cm) ≈ 59.055 in
Summary
Converting 90 centimeters to inches involves applying the conversion factor of 2.54 cm/in. We can perform this conversion using direct calculation or dimensional analysis, both yielding approximately 35.433 inches. However, considering significant figures, a more appropriate answer based on the original measurement's precision would be 35 inches. Understanding this conversion highlights the importance of conversion factors and the power of dimensional analysis in solving unit conversion problems.
Frequently Asked Questions (FAQs)
1. Why is the conversion factor 2.54 cm per inch? This is a defined conversion factor; it's not derived from a physical law but established by agreement between measurement systems.
2. Can I use a different conversion factor? While you can use approximations, using 2.54 cm/in ensures the highest accuracy. Other approximations might lead to inaccuracies in calculations.
3. What if I need to convert inches to centimeters? Simply reverse the conversion factor. Use the fraction 2.54 cm / 1 in.
4. Why is it important to consider significant figures? Significant figures reflect the precision of measurements. Reporting an answer with excessive decimal places implies a higher accuracy than what the original data supports.
5. Are there online converters available? Yes, many online converters are available to instantly convert between centimeters and inches and many other units. However, understanding the mathematical principles behind the conversion is more valuable than relying solely on an online tool.
Note: Conversion is based on the latest values and formulas.
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