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A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
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. Hexadecimal: Base 16, widely used by computer system designers and programmers, as it provides a more human-friendly representation of binary-coded values.
v. t. e. Positional notation, also known as place-value notation, positional numeral system, or simply place value, usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value ...
An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 + 1 / 2 , 5/4 and √ 2 are not. [8] The integers form the smallest group and the smallest ring containing the natural numbers.
Note value. In music notation, a note value indicates the relative duration of a note, using the texture or shape of the notehead, the presence or absence of a stem, and the presence or absence of flags/ beams /hooks/tails. Unmodified note values are fractional powers of two, for example one, one-half, one fourth, etc.
Approximating an irrational number by a fraction π: 22/7 1-digit-denominator Approximating a rational number by a fraction with smaller denominator 399 / 941 3 / 7 1-digit-denominator Approximating a fraction by a fractional decimal number: 5 / 3 1.6667: 4 decimal places: Approximating a fractional decimal number by one with fewer digits 2.1784
In contrast, by the Lindemann–Weierstrass theorem, the sine or cosine of any non-zero algebraic number is always transcendental. [4] The real part of any root of unity is a trigonometric number. By Niven's theorem, the only rational trigonometric numbers are 0, 1, −1, 1/2, and −1/2. [5]
Fractions together with an integer are read as follows: 1 + 1 ⁄ 2 is "one and a half" 6 + 1 ⁄ 4 is "six and a quarter" 7 + 5 ⁄ 8 is "seven and five eighths" A space is placed to mark the boundary between the whole number and the fraction part unless superscripts and subscripts are used; for example: 9 1/2; 9 + 1 ⁄ 2 9 + 1 / 2
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