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6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 1 / 4 , 1 1 / 5 , and 2 − 1 / 9 (i.e., 1 8 / 9 ). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.
Computable number: A real number whose digits can be computed by some algorithm. Period: A number which can be computed as the integral of some algebraic function over an algebraic domain. Definable number: A real number that can be defined uniquely using a first-order formula with one free variable in the language of set theory.
1 ⁄ 7: 0.142... Vulgar Fraction One Seventh 2150 8528 ⅑ 1 ⁄ 9: 0.111... Vulgar Fraction One Ninth 2151 8529 ⅒ 1 ⁄ 10: 0.1 Vulgar Fraction One Tenth 2152 8530 ⅓ 1 ⁄ 3: 0.333... Vulgar Fraction One Third 2153 8531 ⅔ 2 ⁄ 3: 0.666... Vulgar Fraction Two Thirds 2154 8532 ⅕ 1 ⁄ 5: 0.2 Vulgar Fraction One Fifth 2155 8533 ⅖ 2 ...
Often replaced by a horizontal bar. For example, 3 / 2 or . 2. Denotes a quotient structure. For example, quotient set, quotient group, quotient category, etc. 3. In number theory and field theory, / denotes a field extension, where F is an extension field of the field E. 4.
With the restricted definition, each Farey sequence starts with the value 0, denoted by the fraction 0 / 1 , and ends with the value 1, denoted by the fraction 1 / 1 (although some authors omit these terms). A Farey sequence is sometimes called a Farey series, which is not strictly correct, because the terms are not summed. [2]
In Latin and Greek, the ordinal forms are also used for fractions for amounts higher than 2; only the fraction 1 / 2 has special forms. The same suffix may be used with more than one category of number, as for example the orginary numbers secondary and tertiary and the distributive numbers binary and ternary.
Arthur Eddington argued that the fine-structure constant was a unit fraction. He initially thought it to be 1/136 and later changed his theory to 1/137. This contention has been falsified, given that current estimates of the fine structure constant are (to 6 significant digits) 1/137.036. [30]
For example, in duodecimal, 1 / 2 = 0.6, 1 / 3 = 0.4, 1 / 4 = 0.3 and 1 / 6 = 0.2 all terminate; 1 / 5 = 0. 2497 repeats with period length 4, in contrast with the equivalent decimal expansion of 0.2; 1 / 7 = 0. 186A35 has period 6 in duodecimal, just as it does in decimal. If b is an integer base ...