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[[Category:Encyclopedia]] [[wp:Floating point|Floating point]] is a numeric system for approximating real numbers. Each floating-point number stores some ''digits'' and an ''exponent'' (plus a ''sign'', which is either ''1'' or ''-1'') taking the form

: ''value = sign × digits × RADIX^{exponent}''

This design uses a constant ''RADIX'' and limits the maximum number of digits. Calculations are fast but inexact, because the limit on digits causes round-off errors. It should be noted that, with an appropriate ''exponent'', a floating point number can represent a substantial range of integers exactly (though less than the range that could fit in the same space with a “pure” integer).

The most common floating-point formats in modern practice are those based on the [[wp:IEEE 754|IEEE 754]] standard, in particular with the ''RADIX'' being ''2'', and the ''digits'' and ''exponent'' being a fixed number of binary digits that fit (together with the ''sign'') in a piece of memory of size 32 bits (4 bytes, `float`

) or 64 bits (8 bytes, `double`

).