Significand

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The significand (also coefficient or, more informally, mantissa) is the part of a floating-point number that contains its significant digits. Depending on the interpretation of the exponent, the significand may be considered to be an integer or a fraction.

For example, the number 123.45 can be represented as a decimal floating-point number with integer significand 12345 and exponent −2. Its value is given by the formula:

12345 × 10⁻²

This same value could also be represented with the fractional coefficient 1.2345 and exponent +2:

1.2345 × 10⁺²

Use of "mantissa"

The original word used in American English to describe the coefficient of floating-point numbers in computer hardware, later called the significand, seems to have been mantissa (see Burks et al., below), and as of 2005 this usage remains common in computing and among computer scientists. However, this use of mantissa is discouraged by the IEEE floating-point standard committee and by some professionals such as William Kahan and Donald Knuth, because it conflicts with the pre-existing usage of mantissa for the fractional part of a logarithm (see also common logarithm).

The older meaning of mantissa is related to the IEEE's significand in that the fractional part of a logarithm is the logarithm of the significand for the same base, plus a constant depending on the normalization. (The integer part of the logarithm requires no such manipulation to relate to the floating-point exponent.)

The logarithmic meaning of mantissa dates to the 18th century (according to the OED), from its general English meaning (now archaic) of "minor addition", which stemmed from the Latin word for "makeweight" (which in turn may have come from Etruscan). Significand is a 20th century neologism.

References

• Burks, Arthur W.; Goldstine, Herman H.; Von Neumann, John (1946). Preliminary discussion of the logical design of an electronic computing instrument. Technical Report, Institute for Advanced Study, Princeton, NJ. In Von Neumann, Collected Works Vol. 5, A. H. Taub, ed., MacMillan, New York, 1963, p.42:
  
  5.3. "Several of the digital computers being built or planned in this country and England are to contain a so-called "floating decimal point". This is a mechanism for expressing each word as a characteristic and a mantissa—e.g. 123.45 would be carried in the machine as (0.12345,03), where the 3 is the exponent of 10 associated with the number."pt:Significando