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)
There is no time like the present for postponing what you ought to be doing.