# Significand

The

**significand** (also the

*coefficient* or, more informally, the

*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}

The original word for the significand appears to be

*mantissa*, dating at least to the 1940's (see below). This usage of

*mantissa*, while still popular, has been discouraged by the

IEEE floating-point standard committee and professionals such as

William Kahan. It conflicts with an older usage of

*mantissa* for the fractional part of a

logarithm (corresponding to the logarithm of the significand), although this older meaning has grown less common with the disappearance of logarithmic tables in favor of computers.

## Reference

- Arthur W. Burks, Herman H. Goldstine, and John von Neumann,
*Preliminary discussion of the logical design of an electronic computing instrument*, Technical Report, Institute for Advanced Study, Princeton NJ (1946). In J. 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."