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The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
Arithmetic values thought to have been represented by parts of the Eye of Horus. The scribes of ancient Egypt used two different systems for their fractions, Egyptian fractions (not related to the binary number system) and Horus-Eye fractions (so called because many historians of mathematics believe that the symbols used for this system could be arranged to form the eye of Horus, although this ...
The set of all rational numbers, also referred to as "the rationals", [2] the field of rationals [3] or the field of rational numbers is usually denoted by boldface Q, or blackboard bold . A rational number is a real number.
Conversely the period of the repeating decimal of a fraction c / d will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction 2 / 7 has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction 2 / 7 is ...
With decimal arithmetic, final digits of 0 and 5 are avoided; if there is a choice between numbers with the least significant digit 0 or 1, 4 or 5, 5 or 6, 9 or 0, then the digit different from 0 or 5 shall be selected; otherwise, the choice is arbitrary. IBM defines that, in the latter case, a digit with the smaller magnitude shall be selected ...
In binary (base-2), a full space can be used between groups of four digits, corresponding to a nibble, or equivalently to a hexadecimal digit. For integer numbers, dots are used as well to separate groups of four bits. [b] Alternatively, binary digits may be grouped by threes, corresponding to an octal digit.
In many computer systems, binary floating-point numbers are represented internally using this normalized form for their representations; for details, see normal number (computing). Although the point is described as floating , for a normalized floating-point number, its position is fixed, the movement being reflected in the different values of ...
[2] [3] The adjective real, used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of −1. [4] The real numbers include the rational numbers, such as the integer −5 and the fraction 4 / 3. The rest of the real numbers are called irrational numbers.