A calculation can be error-prone. If a small, rounding error
is expanded by later steps (through exponentiation
, for example), then the calculation requires many digits
. If you do not attend to them, the answer will be erroneous. If you do, then the chances of your making an error are multiplied, though your answer will be better than if you ignored them altogether.
Another way a calculation can be error-prone is if it is highly serial. This multiplies the number of calculations involved, and thus multiplies the chance of error.
Lastly, serious errors in human calculation almost never go uncorrected when the human has some intuition about the range the answer should be in. If one multiplies 21.01 by 20.5 and accidentally shifts a place for one of the digits, one could get an answer under 400 or over 450, which would immediately bring one to examine the work rather than accept it.