Some Rules for Getting the Right Answers
0. Many STEM problems involve manipulation of a set of constrained equations. Identify the set for the problem you are solving.
1. The numbers don't matter; so, ... plan on always deriving the formula or mathematical expression for your answer, first.
2. Never operate on or write dimensionless numbers in a derivation or problem solution.
3. VARIABLE = Quantity x [Units]. This is always true, even if its not presented this way in introductory courses.
4. Only variables with the same units can be added (or subtracted).
5. The result of multiplying two variables is has units that are the product of the multiplier and multiplicand:
VARIABLE_1 x VARIABLE_2 = Quantity_1 x Quantity_2 x [Units_1 x Units_2] .
Sometimes, units in the numerator(denominator) of one variable will cancel out units in the denominator(numerator) of the other.
6. For details, Google "Dimensional Analysis". That's what I'm talking about!
7. Corrects answers come from derivation with correct units; plug in the numbers on the next to last line of your solution.
8. If you see a Numerical Example without units in a book or study guide, write your own dimensionally correct version.