Mantissa

WORD OF THE DAY
mantissa \ man-tis-sah \ noun

Definition
1: the part of a logarithm to the right of the decimal point
1b: the logarithm of the significant digits, a decimal fraction between 0 and 1
2: the part of a floating-point number that represents the significant digits of that number, and that is multiplied by the base raised to the exponent to give the actual value of the number.


Examples:
Generally found in a table:
To find the logarithm of 358, one would look up log 3.58 ≅ 0.55388.
Therefore, log 358 = log 3.58 + log 100 = 0.55388 + 2 = 2.55388.


Did You Know?
The general popularity of "Mantissa" is in the bottom 20% of words!  To understand mantissa, one needs to understand a bit about logarithms. The availability of logarithms greatly influenced the form of plane and spherical trigonometry. The procedures of trigonometry were recast to produce formulas in which the operations that depend on logarithms are done all at once. The recourse to the tables then consisted of only two steps, obtaining logarithms and, after performing computations with the logarithms, obtaining antilogarithms
The invention of logarithms was foreshadowed by the comparison of arithmetic and geometric sequences. In a geometric sequence each term forms a constant ratio with its successor; for example,
…1/1,000, 1/100, 1/10, 1, 10, 100, 1,000…
has a common ratio of 10. In an arithmetic sequence each successive term differs by a constant, known as the common difference; for example,
…−3, −2, −1, 0, 1, 2, 3…
has a common difference of 1. Note that a geometric sequence can be written in terms of its common ratio; for the example geometric sequence given above:
…10−3, 10−2, 10−1, 100, 101, 102, 103….
Multiplying two numbers in the geometric sequence, say 1/10 and 100, is equal to adding the corresponding exponents of the common ratio, −1 and 2, to obtain 101 = 10. Thus, multiplication is transformed into addition. The original comparison between the two series, however, was not based on any explicit use of the exponential notation; this was a later development. In 1620 the first table based on the concept of relating geometric and arithmetic sequences was published in Prague by the Swiss mathematician Joost Bürgi.
The Scottish mathematician John Napier published his discovery of logarithms in 1614. His purpose was to assist in the multiplication of quantities that were then called sines. The whole sine was the value of the side of a right-angled triangle with a large hypotenuse. (Napier’s original hypotenuse was 107.) His definition was given in terms of relative rates