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An important property of base-10 logarithms, which makes them so useful in calculations, is that the logarithm of numbers greater than 1 that differ by a factor of a power of 10 all have the same fractional part. The fractional part is known as the mantissa. [b] Thus, log tables need only show the fractional part. Tables of common logarithms ...
The common logarithm of x can be separated into an integer part and a fractional part, known as the characteristic and mantissa. Tables of logarithms need only include the mantissa, as the characteristic can be easily determined by counting digits from the decimal point. [31]
The logarithm in the table, however, is of that sine value divided by 10,000,000. [1]: p. 19 The logarithm is again presented as an integer with an implied denominator of 10,000,000. The table consists of 45 pairs of facing pages. Each pair is labeled at the top with an angle, from 0 to 44 degrees, and at the bottom from 90 to 45 degrees.
The fractional part of logarithms, [2] specifically, is also known as the mantissa; by contrast with the mantissa, the integral part of a logarithm is called its characteristic. [ 3 ] [ 4 ] The word mantissa was introduced by Henry Briggs .
In 1946, Arthur Burks used the terms mantissa and characteristic to describe the two parts of a floating-point number (Burks [11] et al.) by analogy with the then-prevalent common logarithm tables: the characteristic is the integer part of the logarithm (i.e. the exponent), and the mantissa is the fractional part.
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.
Base-10 logarithms have an additional property that is unique and useful: The common logarithm of numbers greater than one that differ only by a factor of a power of ten all have the same fractional part, known as the mantissa. Tables of common logarithms typically included only the mantissas; the integer part of the logarithm, known as the ...
Mantissa (/ m æ n ˈ t ɪ s ə /) may refer to: Mantissa (logarithm), the fractional part of the common (base-10) logarithm; Significand (also commonly called mantissa), the significant digits of a floating-point number or a number in scientific notation; Mantissa (band) Mantissa, a 1982 novel by John Fowles; Mantissa College