estimation is an important skill for real scientists. It is not a "liberal arts plot." Hate to burst your bubble...
If they asked for 2 significant digits, 360 actually is the right answer
I can't tell you the number of times I had students give dumbass answers because they did not understand orders of magnitude or approximation. A good science student should be able to look at a complex equation and give you a quick guestimate of the answer.