Mistakes when working out problems in physics have two common sources: signs (forgetting a number is negative) and units (e.g. using a number thinking it's in meters when in reality, it's in kilometers).
Watching units avoids a good fractions of the mistakes one can make in solving physics problems. This begs the question: Who cares about solving physics problems? Isn't that something one does only in a physics course? If one gets it wrong, it's a low score. In the grand scheme of things, does it matter?
Consider this. When engineers figure out when to fire the thrusters on a space probe and by how much, that's a physics problem. When a flight crew decide how much fuel their airliner needs to make it to its destination with 200 people on board, that's a physics problem. If they get it wrong, the airplane crashes.
In 1999 a NASA mission, the Mars Climate Orbiter, burned up in the martian atmosphere because the spacecraft received thrust instructions in the wrong units. The system designers, who should have been thinking about units, did not. No-one died, but that was 650 Million dollars gone up in smoke and scientists who never got their data and had to look for something else to do.
In 1983 a jet liner ran out of fuel on its way from Montreal to Edmonton, Canada, before reaching its destination because of a mix up with units. The incident is known as the Gimli glider incident. The only reason the occupants survived is because the pilot happened to be a professional large glider pilot. A large glider is exactly what he had to fly when the engines went silent.
The incident would never have happened if the flight crew had taken a physics course or learned the most important lesson from the one they took: ALWAYS WRITE DOWN YOUR UNITS. EVERY STEP OF THE WAY. They would have spotted their mistake on line 1, when they ended up with a weight in pounds instead of the expected kilograms. Then they probably would not have happily deducted that weight in pounds from a weight in kilograms. And even if they did and carried their units to the last step of the calculations, they would have wondered what an amount of fuel in liter times kilograms per pounds means.
