Question

Use unit multipliers to convert 123 pounds per mile to ounces per centimeter. There are 5,280 feet in 1 mile. There are 16 ounces in 1 pound. There are approximately 2.54 cm in 1 inch. Enter your answer as a decimal rounded to the nearest hundredth. Just enter the number.

Answer 1

A unit multiplier is a conversion factor of value 1 that we can use to convert quantities.
We want to convert 123 pounds per mile to ounces per centimeter. 
First, we are going to express the quantity to convert as a fraction:
123 pounds per mile=$123 \frac{pounds}{mile}$

Next, we are going to find our multipliers:
- We know for our problem that there are 5,280 feet in 1 mile, so our first multiplier will be: $\frac{1mile}{5280ft}$
- We also know that there are 16 ounces in 1 pound, so our second multiplier will be: $\frac{16ounces}{1pound}$
- We know that there are 12 inches in 1 foot, so our third multiplier will be: $\frac{1ft}{12in}$
- We know that there are approximately 2.54 cm in 1 inch, so our fourth multiplier will be: $\frac{1in}{2.54cm}$

Now we can put all our multipliers together:
$123 \frac{pounds}{mile} * \frac{1mile}{5280ft}*\frac{16ounces}{1pound}* \frac{1ft}{12in}*\frac{1in}{2.54cm}=0.01 \frac{ounces}{cm}$

We can conclude that the answer is 0.01