The significant part in mathematics as it is a fractional part of a logarithm of number is assigned to a mantissa. It is more detailed understanding of value of a mantissa and its form will help to understand it.
Value of a mantissa
Mantissa - one of parts of number which is presented by a format with a floating point. The second part of this number is the exponent. In fact, it is a fractional component of a logarithm.
The value of a mantissa is that on it there is a number which is a logarithm source. The whole part shows only degree of ten or a trivial multiplier whereas the mantissa shows what number has to be increased by a trivial multiplier which has an appearance 0.001 or 100.
Exponential record presents it in the following form: N = M*n^p where a mantissa is M. For an example it is possible to take number 3600 and to present it in exponential record. The following will turn out: 3600 = 3.6*10^3. Considering the aforesaid, a mantissa will be number 3.6. It is important to understand that the number having a floating comma also has the changing absolute accuracy and the fixed relative accuracy. Use of numbers from a floating comma is better, than representation of numbers from the fixed comma as there is a possibility of use of big range of values whereas relative accuracy does not change. It will help to understand the following example: the form having the fixed comma allows to present number which occupies 2 categories after a comma and 8 categories in the whole part, in the form of 8765.43; 123456.78 and so on. If to take the format having a floating comma it is possible to make the following record: 1.2345678; 0.000012345678 and so on. However so to make, important to have the two-digit additional field allowing to write down exponents 10, beginning from 0 and finishing 1610. Total number of categories will be 10, that is 8+2. The mantissa, both for negative, and for positive numbers, is expressed in a true form. The difference in the sign will be reflected only in value of the sign category. However the mantissa of number cannot exceed units. Usually the point in a mantissa is located on the left side from the senior category. For this purpose, to receive true value of number, it is necessary to increase a mantissa by 16 in order degree. The order received this way is called characteristic. It turns out that characteristic which is counted from 64 will be always positive. In normal record a number mantissa — always a proper fraction. Its record in a cell is made the same as record of number from a comma in a car cell. The comma is fixed before the first category of a digital form. The number mantissa having a floating comma is expressed by hexadecimal figures, at the same time the comma is located to the left of the highest figure of a mantissa
Mantissa form
There are two forms allowing to understand the place of application of a mantissa. The first — a normal form of number. This form which has a mantissa without the sign on a half-interval, that is [0; 1) (0\le a