What you should have done in that one problem was not used a calculator, but looked at the sizes of the numbers given in the multiple choices, and then picked the choice where the magnitude was in the correct ballpark.
Uh, no. If a test question says I can use a calculator, I'm using a calculator. For some of these tests, there's too many questions not to. Obviously, this one was trivial, but you catch my drift. In *most* cases, a calculator is more efficient (yes, you can find some edge cases where realizing the "trick" is faster than typing the equation)