Handling Units

How can you be sure that you've used the right formula and used it correctly? How can you be certain you plugged in the correct data to get the answer you want? One way is to ALWAYS include units with your numbers!

Units multiply and divide ("cancel") the same as algebraic quantities. They can help you see if you have the right form of an equation, or if you've entered data into an equation correctly. The units you plug into a formula must combine to give the units you expect for the answer.

Supposed you want to know how far you will travel in the next 30 minutes if you keep your speed at 62 miles per hour. Since the question is "how far" the answer should be in "miles". Can you multiply 62 miles per hour times 30 minutes and get the answer you are looking for? Of course not- you must know the time of travel in the same units as the time units in the speed. If you look at the equation below, you will see that the units "hour" cancel (they appear in both the numerator and the denominator) and the units you are left with are miles.

If the original time of "30 minutes" had been used, the units would not have cancelled

and the answer would have the odd units mile-minute/hour. Even though the arithmetic is correct, the answer is wrong.

THE MORAL IS: Always include the units with every number in every equation.