## Fact for September 16, 2008 – computational accuracy

Due to the vagaries of rounding, to a calculator or computer that is calculating to, say, eight decimal places,

$((\frac{2}{3})+(\frac{2}{3}))-(\frac{1}{3}) \ne (\frac{2}{3})+((\frac{2}{3})-(\frac{1}{3}))$.

Thus computer arithmetic is not necessarily associative. In this case, while the former ought to come out to 1, the latter will actually be 0.99999997.