To convert between units, you need to know the relationship between units. For example, one mile equals 5280 feet. This relationship can now be used as a conversion factor, set up as required by the question. For each conversion, choose the correct arrangement of the conversion factor and complete the calculation 1. Convert 7860 feet to miles 7860 feet x (A) A: 1 mile B: 5280 feet 7860 feet miles 2. Co 0.5 miles to feet 0.565 miles x (C) TD C: Choose… D: Choose 0.565 miles feet
The Correct Answer and Explanation is:
. Convert 7860 feet to miles
To convert feet to miles, we use the relationship that 1 mile = 5280 feet. Therefore, the conversion factor would be: Conversion Factor=1 mile5280 feet\text{Conversion Factor} = \frac{1 \text{ mile}}{5280 \text{ feet}}Conversion Factor=5280 feet1 mile
Now, for the conversion: 7860 feet×1 mile5280 feet=78605280 miles7860 \text{ feet} \times \frac{1 \text{ mile}}{5280 \text{ feet}} = \frac{7860}{5280} \text{ miles}7860 feet×5280 feet1 mile=52807860 miles
Simplifying the division: 78605280=1.487 miles\frac{7860}{5280} = 1.487 \text{ miles}52807860=1.487 miles
Answer: 7860 feet = 1.487 miles.
Explanation: The unit “feet” cancels out, leaving miles. By performing the division, we determine the equivalent distance in miles.
2. Convert 0.565 miles to feet
To convert miles to feet, we use the relationship that 1 mile = 5280 feet. So the conversion factor would be: Conversion Factor=5280 feet1 mile\text{Conversion Factor} = \frac{5280 \text{ feet}}{1 \text{ mile}}Conversion Factor=1 mile5280 feet
Now, for the conversion: 0.565 miles×5280 feet1 mile=0.565×5280 feet0.565 \text{ miles} \times \frac{5280 \text{ feet}}{1 \text{ mile}} = 0.565 \times 5280 \text{ feet}0.565 miles×1 mile5280 feet=0.565×5280 feet
Multiplying: 0.565×5280=2980.8 feet0.565 \times 5280 = 2980.8 \text{ feet}0.565×5280=2980.8 feet
Answer: 0.565 miles = 2980.8 feet.
Explanation: The unit “mile” cancels out, leaving feet. By multiplying, we determine the equivalent distance in feet.
These calculations show how conversion factors work, ensuring that units cancel out and we’re left with the desired units in the result. In each case, knowing the relationship between the two units—miles and feet—lets us set up the problem correctly for a simple calculation.
