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This decimal format can also represent any binary fraction a/2 m, such as 1/8 (0.125) or 17/32 (0.53125). More generally, a rational number a/b, with a and b relatively prime and b positive, can be exactly represented in binary fixed point only if b is a power of 2; and in decimal fixed point only if b has no prime factors other than 2 and/or 5.
((x),(y) = {239, 13 2} is a solution to the Pell equation x 2 − 2 y 2 = −1.) Formulae of this kind are known as Machin-like formulae . Machin's particular formula was used well into the computer era for calculating record numbers of digits of π , [ 39 ] but more recently other similar formulae have been used as well.
Unit fractions can also be expressed using negative exponents, as in 2 −1, which represents 1/2, and 2 −2, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two, e.g. 1 / 8 = 1 / 2 3 . In Unicode, precomposed fraction characters are in the Number Forms block.
For a positive number written in a conventional positional numeral system (such as binary or decimal), its fractional part hence corresponds to the digits appearing after the radix point, such as the decimal point in English. The result is a real number in the half-open interval [0, 1).
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 ...
In English and many other languages (including many that are written right-to-left), the integer part is at the left of the radix point, and the fraction part at the right of it. [24] A radix point is most often used in decimal (base 10) notation, when it is more commonly called the decimal point (the prefix deci-implying base 10).
For example, replacing $ 23.4476 with $ 23.45, the fraction 312/937 with 1/3, or the expression √2 with 1.414. Rounding is often done to obtain a value that is easier to report and communicate than the original.
Subdivisions of an inch are typically written using dyadic fractions with odd number numerators; for example, two and three-eighths of an inch would be written as 2 + 3 / 8 ″ and not as 2.375″ nor as 2 + 6 / 16 ″. However, for engineering purposes fractions are commonly given to three or four places of decimals and have been ...