I think that the bottom line is that it is fine using aids to calculation but you need to be able to tell if the result is wrong for what ever reason, be it malfunction or user error.
And it doesn't matter if that aid is log tables, slide rule or electronic calculator.
When I was a G.A. in grad school I had a prof who insisted we we sum up test scores in our head, when we graded papers. Since the numbers were never more than two digits, it was pretty easy. However what I do now is take lots and lots of percentage compositions. like 1209.4/5321.8
I really can't see using long division to get the answer.