The ability to convert units of measurement is a fundamental skill in mathematics and science. Understanding how to seamlessly move between different units, like centimeters to meters or inches to feet, is crucial for accurate calculations and clear communication. This article focuses on the conversion of 138 centimeters (cm) to other common units of length, providing a detailed, step-by-step explanation of the mathematical processes involved. This seemingly simple task offers a valuable opportunity to reinforce our understanding of ratios, proportions, and the metric system. We will explore conversions to meters, millimeters, inches, and feet, highlighting the underlying mathematical principles in each case.
Understanding the Metric System:
The metric system, officially known as the International System of Units (SI), is a decimal system based on powers of 10. This makes conversions within the system relatively straightforward. The fundamental unit of length in the metric system is the meter (m). Other units, like centimeters (cm) and millimeters (mm), are derived from the meter. Their relationships are defined as follows:
These relationships are crucial for performing conversions. They represent ratios that can be used in proportional equations.
1. Converting 138cm to Meters (m):
To convert 138 centimeters to meters, we use the conversion factor: 1m = 100cm. This can be expressed as a ratio: 1m/100cm or 100cm/1m. We choose the ratio that allows us to cancel out the 'cm' unit and leave us with 'm'.
Step 1: Set up the conversion equation:
138 cm (1m / 100cm) = x m
Step 2: Cancel out the common units (cm):
138 (1m / 100) = x m
Step 3: Perform the calculation:
(138 / 100) m = x m
x = 1.38 m
Therefore, 138 centimeters is equal to 1.38 meters.
2. Converting 138cm to Millimeters (mm):
The conversion factor here is 1cm = 10mm. Again, we set up a proportional equation to perform the conversion.
Step 1: Set up the conversion equation:
138 cm (10 mm / 1 cm) = x mm
Step 2: Cancel out the common units (cm):
138 10 mm = x mm
Step 3: Perform the calculation:
x = 1380 mm
Therefore, 138 centimeters is equal to 1380 millimeters.
3. Converting 138cm to Inches (in):
Converting between the metric system and the imperial system (used in the US and some other countries) requires a different approach. The conversion factor is approximately 1 inch = 2.54 centimeters.
Step 1: Set up the conversion equation:
138 cm (1 in / 2.54 cm) = x in
Step 2: Cancel out the common units (cm):
138 / 2.54 in = x in
Step 3: Perform the calculation:
x ≈ 54.33 in
Therefore, 138 centimeters is approximately equal to 54.33 inches. Note that this is an approximation due to the approximate nature of the conversion factor.
4. Converting 138cm to Feet (ft):
Since 1 foot = 12 inches, we can use a two-step conversion process. First, we convert centimeters to inches (as shown above), and then convert inches to feet.
Step 1: Convert cm to inches (from previous calculation):
138 cm ≈ 54.33 in
Step 2: Convert inches to feet using the conversion factor 1 ft = 12 in:
54.33 in (1 ft / 12 in) = x ft
Step 3: Cancel out the common units (in) and perform the calculation:
54.33 / 12 ft = x ft
x ≈ 4.53 ft
Therefore, 138 centimeters is approximately equal to 4.53 feet.
Summary:
Converting units of length, as demonstrated with the example of 138cm, involves understanding the relationships between different units and utilizing conversion factors within proportional equations. The metric system simplifies conversions due to its decimal base, while conversions between metric and imperial systems require the use of approximate conversion factors. Mastering these techniques is fundamental for accurate calculations and effective communication in various fields.
FAQs:
1. Why are some conversions approximate? Conversions between metric and imperial units are approximate because the conversion factors (e.g., 1 inch ≈ 2.54 cm) are themselves approximations. They represent a rounded value of a more precise, often irrational, number.
2. Can I use different conversion factors? You can use different conversion factors as long as they are mathematically equivalent. For instance, you could use 1m = 1000mm and then convert mm to cm instead of directly converting cm to m. The final answer should remain consistent.
3. What happens if I use the wrong conversion factor? Using the wrong conversion factor will lead to an incorrect answer. Always double-check that you are using the correct ratio to cancel out the desired units.
4. How can I improve my accuracy in conversions? Use precise conversion factors (as many decimal places as necessary) and use a calculator for calculations. Pay close attention to significant figures to avoid accumulating rounding errors.
5. Are there online tools to assist with unit conversions? Yes, many online calculators and conversion tools are available that can perform unit conversions quickly and accurately. These can be a helpful aid in checking your manual calculations.
Note: Conversion is based on the latest values and formulas.
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