Real world rounding errors
It's not always a mathematical error - sometimes the problem can be a misunderstanding between two parties on how rounding is to be done. In engineering contracts, the tradition is to do all calculations to four decimal places, only rounding to two when a financial value is displayed. Sounds simple enough but there's still plenty of scope for error. For example if something has a value of £1.2486 and you want to use 10 of them, you could round at the beginning to give £1.25 * 10 = £12.50 or round later to give £12.49. A penny doesn't sound much but for using high quantities of a small value (eg 60000 of an item costing 0.0375 could give an error of £150 by the above method). It gets even worse if you have multiple cost lines and vary on whether the rounding is done at the total or individual lines. Finally, how do you round a .5 value? Mathematically (and I believe in banking), the convention is to round to the nearest even digit so 1.5 gets rounded to 2.0, 2.5 gets rounded to 2.0 and 3.5 gets rounded to four. On average, this should give a lesser error. Interestingly, Microsoft isn't even consistent, Excel rounds upwards ROUND(2.5,0)=3 but Access rounds as described above.