Floating point
![An early electromechanical programmable computer, the Z3, included floating-point arithmetic (replica on display at Deutsches Museum in Munich).](/Images/godic/202501/13/Z3_Deutsches_Museum3916.JPG")
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![Integers reinterpreted as floating point numbers (in blue, piecewise linear), compared to a scaled and shifted logarithm (in gray, smooth).](/Images/godic/202501/13/Log_by_aliasing_to_int.svg3917.png")
![William Kahan. A primary architect of the Intel 80x87 floating-point coprocessor and IEEE 754 floating-point standard.](/Images/godic/202501/13/William_Kahan3917.jpg")
In computing, floating point is the formulaic representation that approximates a real number so as to support a trade-off between range and precision. A number is, in general, represented approximately to a fixed number of significant digits (the significand) and scaled using an exponent; the base for the scaling is normally two, ten, or sixteen. A number that can be represented exactly is of the following form: