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16.4.1 Floating-Point Arithmetic Is Not Exact

Binary floating-point representations and arithmetic are inexact. Simple values like 0.1 cannot be precisely represented using binary floating-point numbers, and the limited precision of floating-point numbers means that slight changes in the order of operations or the precision of intermediate storage can change the result. To make matters worse, with arbitrary-precision floating-point arithmetic, you can set the precision before starting a computation, but then you cannot be sure of the number of significant decimal places in the final result.