Notation – the notation of numbers using special symbols, that is, representation of a number in writing. The notation gives the number of a certain standard representation. Depending on the era and field of application has existed and continues to exist many notations.

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**1.** Existing notations can be divided into three main types: positional, mixed and non-positional.

**2.** In positional number systems the symbol or figure can have a different meaning depending on position. The system used is determined by the number of characters. The most popular and the commonly used decimal number system. All numbers are represented by a sequence of ten digits from 0 to 9.

**3.** The operation of the entire digital technology is based on the binary system. It used just two symbols: 1 and 0. All huge set of numbers represented by various combinations of these numbers.

**4.** When certain calculations are applied ternary and octal notations. Also known so-called score by the dozen or duodecimal numeral system. In Informatics and programming is very popular hexadecimal number system, because it allows you to record a machine word is the unit of data when programming.

**5.** Mixed number system is similar to positional. In mixed systems the number presents an increasing sequence. The relationship between the members of this sequence can be completely different.

**6.** So, for the mixed notation can be attributed to the Fibonacci sequence, where each number is the sum of two previous numbers in the sequence, starting with 1. That is, the sequence has the form 1, 1 (1+0), 2 (1+1), 3 (1+2), 5 (2+3) and so on.

**7.** If the entry time in the format: day-hour-minute-second, it is also a mixed notation. Any member of the sequence can be expressed in terms of minimum, i.e. in a second. Often used in mathematics example of a mixed system is also a factorial number system, represented by a sequence of factorials.

**8.** In non-positional number systems the value of a symbol system is fixed and does not depend on its position. These systems are used very rarely, they are mathematically complex. Typical examples of such systems are: the number system stern-brocot, the system of residual classes, a binomial numeral system.

**9.** At different times in different Nations used a variety of number systems. So, for example, very popular had the Roman numeral system, known to this day. It for numbers used the Latin letter V is 5, X Is 10, L is 50, C is 100, D is 500, M is 1000.

**10.** Also these have been known numeral systems as a single, five-part, Babylonian, Jewish, alphabet, ancient Egyptian, Mayan numbers, quipu, Inca.