Computer Numbering Formats
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The term computer numbering formats refers to the schemes implemented in digital computer and calculator hardware and software to represent numbers. A common mistake made by non-specialist computer users is a certain misplaced faith in the infallibility of numerical computations. For example, if one multiplies: scriptstyle 3 times frac13 one might perhaps expect to get a result of exactly 1, which is the correct answer when applying an exact rational number or algebraic model. In practice, however, the result on a digital computer or calculator may prove to be something such as precisely 0.999...
The term computer numbering formats refers to the schemes implemented in digital computer and calculator hardware and software to represent numbers. A common mistake made by non-specialist computer users is a certain misplaced faith in the infallibility of numerical computations. For example, if one multiplies: scriptstyle 3 times frac13 one might perhaps expect to get a result of exactly 1, which is the correct answer when applying an exact rational number or algebraic model. In practice, however, the result on a digital computer or calculator may prove to be something such as precisely 0.9999999999999999 (as one might find when doing the calculation on paper) or, in certain cases, perhaps 0.99999999923475. The latter result seems to indicate a bug, but it is actually an unavoidable consequence of the use of a binary floating-point approximation. Decimal floating-point, computer algebra systems, and certain bignum systems would give either the answer of 1 or 0.9999999999999999 which are equivalent.
