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base-10 real values are represented as character strings in ISO 6093 format; binary real values are represented in a binary format that includes the mantissa, the base (2, 8, or 16), and the exponent; the special values NaN, -INF, +INF, and negative zero are also supported
The integer n is called the exponent and the real number m is called the significand or mantissa. [1] The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the fractional part of the common logarithm. If the number is negative then a minus sign precedes m, as in ordinary decimal notation.
Similar is done by other spreadsheets, the handling of the different amount of decimal digits which can be exactly stored in the 53 bit mantissa of a 'double' (e.g. 16 digits between 1 and 8, but only 15 between 1 / 2 and 1 and between 8 and 10) is somewhat difficult and solved 'suboptimal'.
The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10 −2 power term, also called characteristics, [11] [12] [13] where −2 is the exponent (and 10 is the base). Its value is given by the following arithmetic: 123.45 = 12345 × 10 −2.
In a normal floating-point value, there are no leading zeros in the significand (also commonly called mantissa); rather, leading zeros are removed by adjusting the exponent (for example, the number 0.0123 would be written as 1.23 × 10 −2). Conversely, a denormalized floating point value has a significand with a leading digit of zero.
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Likewise 0.0123 can be rewritten as 1.23 × 10 −2. The part of the representation that contains the significant figures (1.30 or 1.23) is known as the significand or mantissa. The digits in the base and exponent (10 3 or 10 −2) are considered exact numbers so for these digits, significant figures are irrelevant.