TITLE: How precise should an absolute error be?
QUESTION [3 upvotes]: While adding approximate numbers, our result must be as precise as the least precise number that was given to us.
For instance, $101+1.001+1.0≈103$ because the number with the least precision viz., $101$, is correct to the nearest unit.
But what about when evaluating errors? Suppose $2/3$ is approximated to $0.6667$. Then the absolute error would be $|2/3-0.6667|$. But this value is $0.00003333333...$, which, according to our rules, we must approximate to $0.0000$ (as precise as $0.6667$). 
This is certainly not right.

REPLY [1 votes]: Thats right, with an absolute error of $0.0001$, 
$$\left|\frac23-0.6667\right|=0.0000$$
{"set_name": "stack_exchange", "score": 3, "question_id": 2514388}