My book says: The bit I don't get is Why? Apply this logic to one of the numbers at random for arguments sake, let's say the first number .234673, it couldn't be .2346735-.2346739 or else it would have been rounded to .234674. It's true value (if it's greater) has to lie somewhere between .2346731-2346734 or else it would have been rounded up to .234674 . So if it can't be .0000005 greater as that would get it rounded up to .234674, and you can't count .2346730 when calculating error as .2346730 is the same as .234673 which would be correct and wouldn't be a possible error you have to factor in, then knowing the figures are accurate to 6 significant figures it would appear to me that logically the possible error range is .2346731-.2346734 = .0000004 greater .2346725-.2346729 = .0000005 lesser And this would apply to all 4 figures, so the sum could be (4 X .0000005) -.000002 lesser or (4X.0000004) .0000016 greater. Now it's in the book so obviously there's a flaw in my reasoning and since this is very basic math it's probably a very basic error so that's my question, thanks for reading and I apologize for the longwindedness.