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:
Correct Answers:
- Convert 7860 feet to miles
Use the conversion factor:
1 mile = 5280 feet
To convert feet to miles, divide by 5280:
7860 feet×(1 mile5280 feet)=78605280≈1.49 miles7860 \, \text{feet} \times \left( \frac{1 \, \text{mile}}{5280 \, \text{feet}} \right) = \frac{7860}{5280} \approx 1.49 \, \text{miles}7860feet×(5280feet1mile)=52807860≈1.49miles
Answer:
7860 feet × (1 mile / 5280 feet) = 1.49 miles
- Convert 0.565 miles to feet
Use the same conversion factor:
1 mile = 5280 feet
To convert miles to feet, multiply by 5280:
0.565 miles×(5280 feet1 mile)=2983.2 feet0.565 \, \text{miles} \times \left( \frac{5280 \, \text{feet}}{1 \, \text{mile}} \right) = 2983.2 \, \text{feet}0.565miles×(1mile5280feet)=2983.2feet
Answer:
0.565 miles × (5280 feet / 1 mile) = 2983.2 feet
Explanation
When converting between units, you must multiply by a conversion factor, which is a fraction that equals 1 but is written using two equivalent values in different units. For example, since 1 mile is equal to 5280 feet, the conversion factor can be either:
- 1 mile5280 feet\frac{1 \, \text{mile}}{5280 \, \text{feet}}5280feet1mile (to convert from feet to miles), or
- 5280 feet1 mile\frac{5280 \, \text{feet}}{1 \, \text{mile}}1mile5280feet (to convert from miles to feet)
In the first question, you are given 7860 feet and asked to convert to miles. Since feet is the unit you want to cancel out, you place it in the denominator of your conversion factor. That’s why you use 1 mile5280 feet\frac{1 \, \text{mile}}{5280 \, \text{feet}}5280feet1mile. Multiplying 7860 by this fraction gives you the number of miles: 7860÷5280≈1.49 miles7860 \div 5280 \approx 1.49 \, \text{miles}7860÷5280≈1.49miles
In the second question, you are given 0.565 miles and asked to convert to feet. This time, you want to cancel out miles, so you place miles in the denominator. The conversion factor is 5280 feet1 mile\frac{5280 \, \text{feet}}{1 \, \text{mile}}1mile5280feet, and you multiply: 0.565×5280=2983.2 feet0.565 \times 5280 = 2983.2 \, \text{feet}0.565×5280=2983.2feet
This method works for any unit conversion as long as you know the relationship between the two units and set the conversion factor up correctly.
