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Where numerator and denominator can each be expressed in one word, a fraction is usually spelled out (e.g. a two-thirds majority; moved one-quarter mile); use figures if a fraction appears with a unit symbol (e.g. 1 ⁄ 4 mi (markup: {{frac|1|4}} mi), not a quarter of a mi or one-quarter mi).
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 ...
Machin's particular formula was used well into the computer era for calculating record numbers of digits of π, [40] but more recently other similar formulae have been used as well. For instance, Shanks and his team used the following Machin-like formula in 1961 to compute the first 100,000 digits of π: [40]
Given real numbers x and y, integers m and n and the set of integers, floor and ceiling may be defined by the equations ⌊ ⌋ = {}, ⌈ ⌉ = {}. Since there is exactly one integer in a half-open interval of length one, for any real number x, there are unique integers m and n satisfying the equation
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