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Approximate calculation is both development opportunity for, and threat to, one's intellectual integrity.

There are temptations to discard inconvenient uncertainty, to warp calculation to match expectation, to hide calculation failure (especially when doing demonstrations), to neglect to cross check results. You are often dependent on the integrity of your process, with little of the kind of independent check where the universe bites you hard and points out that you have been lying to yourself.

As approximate calculation becomes part of your everyday life, it can either constantly reinforce self honesty, or constantly corrupt it. You can either place your pride in your process, or misplace it in false successes. While elsewhere, perhaps, self deception can be a tool of some use, its concequences in approximate calculation are major, and thus I suggest carefully avoiding it.

From Feynman's Cargo Cult Science:

[...] It's a kind of scientific integrity, a principle of scientific thought that corresponds to a kind of utter honesty--a kind of leaning over backwards. For example, if you're doing an experiment, you should report everything that you think might make it invalid--not only what you think is right about it: other causes that could possibly explain your results; and things you thought of that you've eliminated by some other experiment, and how they worked--to make sure the other fellow can tell they have been eliminated. Details that could throw doubt on your interpretation must be given, if you know them. You must do the best you can--if you know anything at all wrong, or possibly wrong--to explain it. If you make a theory, for example, and advertise it, or put it out, then you must also put down all the facts that disagree with it, as well as those that agree with it. [...] In summary, the idea is to give all of the information to help others to judge the value of your contribution; not just the information that leads to judgment in one particular direction or another. [...] But this long history of learning how to not fool ourselves--of having utter scientific integrity--is, I'm sorry to say, something that we haven't specifically included in any particular course that I know of. We just hope you've caught on by osmosis The first principle is that you must not fool yourself--and you are the easiest person to fool. So you have to be very careful about that. After you've not fooled yourself, it's easy not to fool other scientists. You just have to be honest in a conventional way after that.