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"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
where nnnn is the code point in decimal form, and hhhh is the code point in hexadecimal form. The x must be lowercase in XML documents. The nnnn or hhhh may be any number of digits and may include leading zeros. The hhhh may mix uppercase and lowercase, though uppercase is the usual style.
For example, decimal 365 (10) or senary 1 405 (6) corresponds to binary 1 0110 1101 (2) (nine bits) and to ternary 111 112 (3) (six digits). However, they are still far less compact than the corresponding representations in bases such as decimal – see below for a compact way to codify ternary using nonary (base 9) and septemvigesimal (base 27).
For example, "11" represents the number eleven in the decimal or base-10 numeral system (today, the most common system globally), the number three in the binary or base-2 numeral system (used in modern computers), and the number two in the unary numeral system (used in tallying scores). The number the numeral represents is called its value.
An example of a fraction that cannot be represented by a decimal expression (with a finite number of digits) is 1 / 3 , 3 not being a power of 10. More generally, a decimal with n digits after the separator (a point or comma) represents the fraction with denominator 10 n , whose numerator is the integer obtained by removing the separator.
A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for the thousands separator used in digit grouping.
Decimal: The standard Hindu–Arabic numeral system using base ten. Binary: The base-two numeral system used by computers, with digits 0 and 1. Ternary: The base-three numeral system with 0, 1, and 2 as digits. Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits.
The set of rational numbers is not complete. For example, the sequence (1; 1.4; 1.41; 1.414; 1.4142; 1.41421; ...), where each term adds a digit of the decimal expansion of the positive square root of 2, is Cauchy but it does not converge to a rational number (in the real numbers, in contrast, it converges to the positive square root of 2).