The distance between Saint Louis to Kansas City is 243 miles. What is this distance in feet? (Note: There are 5,280 feet in one mile)

Question

Quizplus · Accepted Answer

In order to convert between different units of measurement, we use what is called a conversion factor. A conversion factor is a ratio (written as a fraction) where one of the units is the numerator and one is the denominator. In order to convert one type of unit to another, you will cross-multiply the starting value by the conversion factor. *We decide which unit goes on the top based on what we are trying to convert. Basically, the units have to match - the units of one numerator should be the same as the numerator of the second fraction. In this case, we know the conversion factor to be the number of feet in one mile. This can be written as either of the following: ^{1 mi} / _{5280 ft} OR ^{5280 ft} / _{1 mi} These can both be used as conversion factors because the ratio of feet to miles is the SAME in both. In order to decide which version to use, we come to our problem. We are told that the distance is 243 miles, and we're trying to convert the miles to feet. Since the number of feet (the distance in feet) is unknown, we're going to represent it as x. In order to solve using ratios, we need to write the first ratio as a fraction. We know that the distance in miles is 243 mi, so that will be the numerator in our fraction (ratio) to start. We have decided to use x to represent the unknown number of feet, so our fraction (ratio) will look like this: ^{243 miles}/_x Now, we know which version of the conversion factor to use. Miles is the unit used in the numerator, so we will use the conversion factor that also has miles in the numerator: ^{1 mi}/_{5280 feet} Now we can set the ratios equal to one another in preparation to solve. ^{243 mi}/_x= ^{1 mi}/_{5280 feet} Now, we can move forward and solve. Cross multiply across the equal sign to eliminate the ratios. This means you multiply the first numerator by the second denominator, and the first denominator by the second numerator. 243 mi • 5280 ft = x • 1mi 1,283,040 mi • ft = x • 1mi Now, we can see that we have the 1mi multiplying the x, so we have to divide both sides by 1mi . Note that when you divide, you also divide by the units. This cancels out the m on the left hand side as well. 1,283,040 mi • ft ÷ 1mi = x • 1mi ÷ 1mi 1,283,040 ft = x Answer: 1,283,040 ft= 243 mi

The Distance Between Saint Louis to Kansas City Is 243