Units: a True Story
A student at an Ivy League university is taking a final exam in an advanced Astrophysics course. She reads a problem similar to the following:
What is the mean free path of a photon through a cloud with optical depth T = 1, electron number density D = 1016 cm-3, and scattering cross-section s = 0.6 ×10-24 cm2?
A sense of panic comes over her as she realizes that, for all her studying, she has no idea how to do this problem. She reads it once more and notes that if she just multiplies the numbers together and takes the reciprocal, the units work out so that the answer has the unit of length, which is what she knows the unit of the answer should be. Knowing that time is running out and she still has to do other problems on the final, she multiplies the numbers (showing her work) and writes down the answer.
Two weeks later, she gets her final exam back and sees that she earned full credit for the problem.
The moral of the story: units are a powerful problem-solving tool. Use them. Units are your friend.