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Chapter 2: Problem 23

Which is the greater distance, 50 miles or 100 kilometers?

Short Answer

Expert verified
50 miles is approximately 80.467 kilometers. Since 100 kilometers is greater than 80.467 kilometers, the greater distance is 100 kilometers.

Step by step solution

01

Convert miles to kilometers

To convert 50 miles to kilometers, we can use the conversion factor of 1 mile = 1.60934 kilometers, setting up a proportion: \(50 \,miles \times \frac{1.60934 \,km}{1 \,mile}\)
02

Multiply

Next, multiply 50 miles by the conversion factor: \(50 \times 1.60934 = 80.467\) Now we have calculated that 50 miles is equal to approximately 80.467 kilometers.
03

Comparison

Now that we have the converted distance, we can compare it to 100 kilometers. Comparing 80.467 kilometers (the 50-mile distance) and 100 kilometers, we can see that: 100 kilometers > 80.467 kilometers So, 100 kilometers is the greater distance.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Miles to Kilometers Conversion
Converting miles to kilometers is a common task in measurement conversion. Whether you're traveling, calculating environmental data, or simply curious, knowing how to convert these units can be very useful. Here's how it works:
  • A mile is longer than a kilometer. Specifically, one mile is approximately equal to 1.60934 kilometers.
  • To convert miles to kilometers, multiply the number of miles by 1.60934. This constant represents the number of kilometers per mile.
  • In our example, 50 miles is equivalent to 50 multiplied by 1.60934, which is about 80.467 kilometers.
Understanding and using this conversion factor allows you to easily switch between the two units. This is particularly useful when working with international data or traveling.
Comparing Distances Measured in Different Units
Sometimes, you need to compare two distances that are measured in different units, like miles and kilometers. But directly comparing numbers measured with different units, like 50 miles and 100 kilometers, isn't effective.
  • Firstly, convert all measurements to the same unit. This usually involves some math, like using the conversion factor mentioned earlier.
  • After converting, the numbers can be directly compared. In the exercise, 50 miles was converted to 80.467 kilometers.
  • We then compared 80.467 kilometers to 100 kilometers. It's obvious that 100 kilometers is greater.
This method allows you to effectively determine which of two distances is greater, which is particularly helpful in many practical scenarios.
The Process of Measurement Conversion
Measurement conversion is an essential skill in mathematics and sciences. It allows you to compare quantities that appear different but are related through a conversion factor.
  • Identify the exact conversion factor needed for your specific units. For miles to kilometers, this factor is 1.60934.
  • Always ensure that your measurements are in the correct form for conversion; use multiplication or division as needed.
  • In this case, you multiplied miles by the conversion factor to get kilometers.
Measurement conversion is common in fields such as engineering, science, and global commerce, as it ensures consistency and understanding in data interpretation across different domains.

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