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Chapter 6: Problem 37

Change \(3.6\) miles to feet.

Short Answer

Expert verified
3.6 miles is 19008 feet.

Step by step solution

01

Understand the Conversion Factor

To convert miles to feet, we need to use the conversion factor: 1 mile is equivalent to 5280 feet. This means we will multiply the number of miles by 5280 to find out how many feet are in that distance.
02

Set Up the Calculation

We need to multiply 3.6 miles by the conversion factor of 5280 feet per mile to find the equivalent distance in feet. The equation looks like this: \[3.6 \text{ miles} \times 5280 \text{ feet/mile}\]
03

Perform the Multiplication

Calculate the multiplication: \[3.6 \times 5280 = 19008\]This result represents the number of feet in 3.6 miles.
04

State the Solution

We have determined that 3.6 miles is equal to 19008 feet.

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Key Concepts

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

Miles to Feet Conversion
When you need to convert miles into feet, knowing the basic units and equivalence is essential. In many situations, you might be given a distance in miles but need to know how long that same distance is in feet.
To do this, first understand that a mile is much longer than a foot. Specifically, 1 mile is equal to 5280 feet. This is a fixed value and will remain the same regardless of the context.
  • Whenever converting miles to feet, think of multiplying by 5280.
  • This is because there are 5280 units of feet in a single mile.
Being comfortable with this conversion means you're well-prepared to tackle other similar conversion tasks.
Conversion Factor
The conversion factor is a critical aspect of converting units from one to another. In unit conversions, a conversion factor bridges the gap between two different units. Here, our conversion factor is 5280 feet per mile.
This factor serves as a consistent multiplier that allows you to switch a measurement from miles to feet easily.
  • A conversion factor is essentially a ratio expressing how many of one unit is equivalent to another.
  • In the mile to feet conversion, this factor remains consistent: 1 mile to 5280 feet.
Utilizing the conversion factor, you can convert any number of miles into feet with precision.
Multiplication in Conversions
To perform a conversion using a conversion factor, you'll rely on multiplication. Every time you convert from miles to feet, you'll start with the given number of miles and multiply it by the conversion factor of 5280.
This is because the conversion factor acts as the standard by which units are changed.
  • For instance, converting 3.6 miles to feet involves multiplying:
  • Take the distance in miles and multiply by 5280 feet per mile.
In our example, \[3.6\, ext{miles} \times 5280\, ext{feet/mile} = 19008\, ext{feet}\]This ensures an accurate and efficient conversion from miles to feet.

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