Perfect accuracy is an insane goal. Much better is to develop the skill of finding and correcting your mistakes. Part of this is doing frequent "sanity checks"

Perfect accuracy is an insane goal. Much better is to develop the skill of finding and correcting your mistakes. Part of this is doing frequent "sanity checks" - for instance, if you are computing an area, and you get the answer -3, probably you made an algebra mistake somewhere earlier, and you should find and fix it before going on (some ways of checking your work also help you pinpoint where the mistake occurred, others are less helpful for that). Another way to check your work is to try plugging in numerical values for all of the variables and going through the arithmetic to check all of the steps (if you need to check your arithmetic, try something like "casting out 9s"). Learning to find and correct your mistakes will at first make it take ten times as long to solve any problem as just scribbling your way to an answer. But if you practice it, you will discover two things: - with practice, the overhead of finding and correcting mistakes drops significantly, - the feedback you get from noticing your mistakes helps you avoid making those mistakes in the future. Eventually mistakes become extremely rare, and you can go through a very long computation without making a mistake, even if you don't bother checking for them any more!