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The repeating sequence of digits is called "repetend" which has a certain length greater than 0, also called "period". [5] In base 10, a fraction has a repeating decimal if and only if in lowest terms, its denominator has any prime factors besides 2 or 5, or in other words, cannot be expressed as 2 m 5 n, where m and n are non-negative integers.
However, most decimal fractions like 0.1 or 0.123 are infinite repeating fractions in base 2. and hence cannot be represented that way. Similarly, any decimal fraction a /10 m , such as 1/100 or 37/1000, can be exactly represented in fixed point with a power-of-ten scaling factor 1/10 n with any n ≥ m .
Stylistic impression of the repeating decimal 0.9999..., representing the digit 9 repeating infinitely. In mathematics, 0.999... (also written as 0. 9, 0.., or 0.(9)) is a repeating decimal that is an alternative way of writing the number 1.
This distribution is symmetric about its midpoint, with raw moments of about m 1 = 0.5, m 2 = 0.290926, m 3 = 0.186389 and m 4 = 0.126992, [13] and so a mean and median of 0.5, a standard deviation of about 0.2023, a skewness of 0, and an excess kurtosis about −1.147.
A simple fraction (also known as a common fraction or vulgar fraction) [n 1] 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 .
A vinculum can indicate a line segment where A and B are the endpoints: ¯. A vinculum can indicate the repetend of a repeating decimal value: . 1 ⁄ 7 = 0. 142857 = 0.1428571428571428571...
Fraction Percentage Percent sign; Continued fraction ... Repeating decimal; Irrational number ... Prenex normal form. Skolem normal form;
Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general. Other fractional arguments can be approximated through efficient infinite products, infinite series, and recurrence relations.