Decoding the Metric-Imperial Maze: Converting 170 cm to Feet and Inches
The world uses two primary systems for measuring length: the metric system (based on meters) and the imperial system (based on feet and inches). While the metric system is predominantly used globally for its simplicity and logical base-10 structure, the imperial system remains prevalent in certain countries, notably the United States. This often necessitates conversions between the two systems. This article focuses on converting 170 centimeters (cm), a metric unit of length, into feet (ft) and inches (in), units of the imperial system. Understanding this conversion process highlights fundamental mathematical principles of unit conversion and ratio manipulation, applicable far beyond just length measurements.
Step 1: Understanding the Conversion Factors
The cornerstone of any unit conversion is the conversion factor. This factor establishes the equivalence between the units involved. For our conversion, we need the relationship between centimeters and inches, and then inches and feet.
Centimeters to Inches: 1 inch (in) is equal to 2.54 centimeters (cm). This means that there are 2.54 cm in every 1 inch. We can express this as a conversion factor: (1 in / 2.54 cm) or (2.54 cm / 1 in). The choice of which fraction to use depends on which unit we want to eliminate.
Inches to Feet: 1 foot (ft) is equal to 12 inches (in). This gives us the conversion factors: (1 ft / 12 in) or (12 in / 1 ft). Again, the correct choice depends on our cancellation strategy.
Step 2: Converting Centimeters to Inches
We start with 170 cm and want to convert it to inches. Since we want to eliminate centimeters and end up with inches, we use the conversion factor (1 in / 2.54 cm). We set up the conversion as follows:
170 cm × (1 in / 2.54 cm)
Notice how the "cm" units cancel each other out:
170 × (1 in / 2.54) = (170/2.54) in
Performing the division:
170 / 2.54 ≈ 66.93 in
Therefore, 170 cm is approximately 66.93 inches.
Step 3: Converting Inches to Feet and Inches
Now we have 66.93 inches and need to convert this into feet and inches. Since there are 12 inches in a foot, we divide the total number of inches by 12 to find the number of feet:
66.93 in / 12 in/ft ≈ 5.58 ft
This tells us that there are approximately 5 whole feet. To find the remaining inches, we take the decimal part of the result (0.58) and multiply it by 12:
0.58 ft × 12 in/ft ≈ 6.96 in
Therefore, 66.93 inches is approximately 5 feet and 6.96 inches.
Step 4: Rounding and Final Answer
Since we're dealing with measurements, rounding is often necessary. Rounding 6.96 inches to the nearest tenth of an inch gives us 7 inches.
Therefore, 170 cm is approximately equal to 5 feet and 7 inches.
Step 5: Alternative Approach – Single Calculation
We can combine steps 2 and 3 into a single calculation. We use both conversion factors:
170 cm × (1 in / 2.54 cm) × (1 ft / 12 in)
Notice that "cm" and "in" cancel, leaving only "ft":
170 / (2.54 × 12) ft ≈ 5.58 ft
This again gives us approximately 5.58 feet. The remaining inches are calculated as before: 0.58 ft 12 in/ft ≈ 7 in.
Summary:
Converting 170 cm to feet and inches involves a two-step (or combined single-step) process using conversion factors. We first convert centimeters to inches using the factor 1 in / 2.54 cm, then convert inches to feet and inches using the factor 1 ft / 12 in. Through careful unit cancellation and arithmetic operations, we determined that 170 cm is approximately 5 feet and 7 inches. This demonstrates the practical application of mathematical concepts like unit conversion and ratio manipulation in everyday situations.
Frequently Asked Questions (FAQs):
1. Why are there two different systems of measurement? Historically, different regions developed their own measurement systems, leading to the coexistence of the metric and imperial systems. While the metric system offers greater simplicity and consistency, the imperial system persists due to historical reasons and inertia in some countries.
2. Can I use a calculator for this conversion? Absolutely! Calculators simplify the arithmetic involved, especially when dealing with decimal numbers. However, understanding the underlying mathematical principles remains crucial.
3. What is the exact conversion of 170 cm to feet and inches? There is no perfectly exact conversion because the relationship between centimeters and inches (2.54 cm per inch) is a defined constant, but the conversion to feet and inches involves rounding. The closest whole number approximation is 5 feet 7 inches.
4. What if I need to convert other units of length? The same principles of unit conversion apply to other units. You'll need the appropriate conversion factors between the units involved (e.g., meters to yards, kilometers to miles).
5. Why is it important to cancel units during the conversion process? Unit cancellation ensures that the conversion is performed correctly. By canceling out the unwanted units (cm and in in this case), we guarantee that the final answer is expressed in the desired units (feet and inches). It acts as a powerful check for errors.
Note: Conversion is based on the latest values and formulas.
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