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Make the indicated unit conversions. Express \(0.225 \mathrm{km}\) in feet

Short Answer

Expert verified
0.225 km = 738.189 feet.

Step by step solution

01

Understand the conversion pathway

To convert kilometers to feet, we first need to convert kilometers to meters, and then convert meters to feet. This can be done using the conversion factors: 1 kilometer = 1000 meters and 1 meter = 3.28084 feet.
02

Convert kilometers to meters

Start by converting the given distance from kilometers to meters. Multiply 0.225 kilometers by 1000 to convert it into meters: \[0.225 \text{ km} \times 1000 = 225 \text{ meters}\]
03

Convert meters to feet

Now, convert the distance from meters to feet using the conversion factor 1 meter = 3.28084 feet:\[225 \text{ meters} \times 3.28084 = 738.189 \text{ feet}\]
04

Present the final answer

After performing the calculations, the distance of 0.225 kilometers is equal to approximately 738.189 feet.

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Key Concepts

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

Kilometers to Meters
Converting kilometers to meters is a straightforward process that often serves as the first step in larger conversion tasks. To convert kilometers into meters, it's important to know the conversion factor. One kilometer is exactly equal to 1000 meters.
  • To make the conversion, you simply multiply the number of kilometers by 1000.
  • This converts the larger measurement unit, kilometers, into the smaller unit, meters.
For example, if you have a distance of 0.225 kilometers, you can find the equivalent distance in meters by calculating:\[0.225 \text{ km} \times 1000 = 225 \text{ meters}\] This step is key in a series of conversions that may further translate the measurement into other units, such as feet.
Meters to Feet
Once you've converted your kilometers to meters, you might need to convert the measurement further into feet. This is typical when working in contexts where imperial units are used, such as in the United States. To convert meters into feet, you'll use the conversion factor that relates these two units: 1 meter equals approximately 3.28084 feet.
  • This is a crucial conversion factor that provides a bridge between the metric and imperial systems.
  • Knowing this allows you to handle measurements in contexts that require different units.
For instance, to convert 225 meters to feet, you perform the following calculation:\[225 \text{ meters} \times 3.28084 = 738.189 \text{ feet}\] This tells you that 225 meters equals approximately 738.189 feet, providing an answer in a unit that may be more familiar or useful depending on the application.
Conversion Factors
Conversion factors are essential tools in unit conversion. They serve as the "translation guides" between units, allowing for accuracy in communication and measurement across different systems. When dealing with conversions, it's vital to know and correctly apply these factors.Here's what you should keep in mind:
  • Conversion factors are constants, which means once they're established, they don't change.
  • Each conversion factor directly relates two units of measurement, such as kilometers to meters, or meters to feet.
  • To convert a measurement, multiply by the appropriate conversion factor.
For example, to convert kilometers to meters, use the factor 1000 meters per kilometer:\[ ext{distance in meters} = ext{distance in kilometers} \times 1000 \text{ meters/kilometer} \]And to convert from meters to feet:\[ ext{distance in feet} = ext{distance in meters} \times 3.28084 \text{ feet/meter} \]Knowing these factors and how to use them ensures you can effectively switch between different measurement systems with ease and accuracy. Always double-check your calculations to ensure precision, especially in fields where accurate measurements are critical.

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