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 × ( A ) ( B ) A: Choose… B: Choose… 7860 feet= miles 2. Convert 0.565 miles to feet 0.565 miles × ( C ) ( D ) C: Choose… D: Choose… 0.565 miles= feet
The Correct Answer and Explanation is:
Correct Answers:
- Convert 7860 feet to miles
7860 feet × (1 mile / 5280 feet) = 1.49 miles- A: 1 mile
- B: 5280 feet
- Convert 0.565 miles to feet
0.565 miles × (5280 feet / 1 mile) = 2983.2 feet- C: 5280 feet
- D: 1 mile
Explanation :
Unit conversion involves multiplying a given quantity by a conversion factor that equals one. This process allows the original units to cancel out, leaving the desired units behind. A conversion factor is a fraction in which the numerator and denominator represent the same quantity in different units. For example, since 1 mile equals 5280 feet, both of the following fractions equal one:
- (1 mile / 5280 feet)
- (5280 feet / 1 mile)
In the first question, you are given a measurement in feet (7860 feet) and are asked to convert it to miles. Since 1 mile = 5280 feet, use the fraction that places miles in the numerator and feet in the denominator:
7860 feet × (1 mile / 5280 feet).
This setup cancels out “feet,” and you are left with miles. Doing the calculation:
7860 ÷ 5280 = 1.49 miles (rounded to two decimal places).
In the second question, you are given miles (0.565) and asked to convert to feet. You use the reverse conversion factor:
0.565 miles × (5280 feet / 1 mile).
This cancels out “miles” and gives you the result in feet.
0.565 × 5280 = 2983.2 feet.
Understanding which way to set up the fraction is key: the unit you want to cancel should be opposite of where it is in your original value. This way, units cancel properly and you’re left with the desired measurement. Proper setup ensures accuracy in any scientific or real-world application involving unit conversions
