As follows is an example from a video tutorial on unit conversions at Khan Academy, an acclaimed open-source education site.
Converting dosages is an everyday skill nurses must have; however, our children learn similar problems in middle and school.
A doctor orders a patient weighing 72.7 kg is to receive 5 mg/lb of Drug X twice a day. The pharmacy administers the drug in a liquid solution whose concentration is 0.9 g/mL. How many milliliters of solutions must the nurse administer to the patient per dose?
A quick look at the numbers and units tells us that we are dealing with mixed units: pounds and kilograms.
Step One: Convert 5 mg/lb to mg/kg.
Sal shows us how to multiply the given dose, 5 mg/lb, by 2.2 lbs./kg. To solve this part of the problem one must know the conversion factor between pounds and kilograms. We have to memorize or look up the conversion.
After we get rid of the U.S. customary units, we can work on the rest of the problem in all metric units.
Step Two: Convert mg/kg to g/kg.
We can see the elegant simplicity of converting between metric units—a base-10 system. Multiply 11 mg/kg by 1/1000 g/mg. We don’t have to memorize the conversion factor once we internalize the metric prefixes. We know “milli” is 1/1000th, so there must be 1000 milligrams in 1 gram.
By contrast, converting within U.S. customary units is positively messy. Do you know how many yards are in a mile?
Here is another word problem from the Khan Academy site:
How many complete laps would Sally need to run around a track that is 300 yards per lap, to run at least 2 miles?
Step One: Convert miles to feet. 
Of course we have to know how many feet in a mile.
Step Two: Convert feet to yards. 
Step Three: Calculate how many full circuits around the track it will take to run at least two miles.
WAIT! Isn’t Step 3 essentially the original problem? Yet we had to go through two conversion steps to get the heart of problem.
What if we only used the metric system? This multi-step word problem boils down to one step.
Sally is training to do a 5K Charity run. Twice a week she runs 4.3 kilometers from work to home. This week she is going to condition at the high school track, which is 250 meters around. How many laps must she run to finish at least 4.3 kilometers?
(4300 m)/(250 m)= 17.2 Laps
Knowing there is 1000 meters in a kilometer allows us to easily convert from kilometers to meter. We tack on two zeros. Then we divide. Sally has to run 18 full laps to complete her goal of running 4.3 kilometers at the track.