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 (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:
`(1mile)/(5280ft)`
- We also know that there are 16 ounces in 1 pound, so our second multiplier will be:
`(16ounces)/(1pound)`
- We know that there are 12 inches in 1 foot, so our third multiplier will be:
`(1ft)/(12in)`
- We know that there are approximately 2.54 cm in 1 inch, so our fourth multiplier will be:
`(1in)/(2.54cm)`

Now we can put all our multipliers together:

`123 (pounds)/(mile) * (1mile)/(5280ft)*(16ounces)/(1pound)* (1ft)/(12in)*(1in)/(2.54cm)=0.01 (ounces)/(cm)`

We can conclude that the answer is 0.01