# Changes

Floating point arithmetic is an approximation '''in binary''' to arithmetic on real or complex numbers. Just like you cannot represent 1/3 exactly in decimal arithmetic (0.333333 is only a rough approximation to 1/3), you cannot represent some decimals like 0.1 exactly in base 2. In binary, the representation to one tenth is $0.\overline{00011}$ where the bar indicates that it repeats infinitely (like how $1/3 = 0.\overline{3}$ in decimal). Because this infinite repetition cannot be represented exactly, rounding errors occur for values that appear to be exact in decimal but are in fact approximations in binary, such as for example how 0.3 - 0.2 - 0.1 is not equal to zero.