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The simplest fraction 3 / y with a three-term expansion is 3 / 7. A fraction 4 / y requires four terms in its greedy expansion if and only if y ≡ 1 or 17 (mod 24), for then the numerator −y mod x of the remaining fraction is 3 and the denominator is 1 (mod 6). The simplest fraction 4 / y with a four-term expansion is 4 / 17.
Borwein and Zucker have found that Γ(n / 24) can be expressed algebraically in terms of π, K(k(1)), K(k(2)), K(k(3)), and K(k(6)) where K(k(N)) is a complete elliptic integral of the first kind. This permits efficiently approximating the gamma function of rational arguments to high precision using quadratically convergent arithmetic ...
One half is a rational number that lies midway between nil and unity (which are the elementary additive and multiplicative identities) as the quotient of the first two non-zero integers, . It has two different decimal representations in base ten, the familiar and the recurring , with a similar pair of expansions in any even base; while in odd ...
1400 (3.878 × 10 19 kg) 1.39: 0.000 125: 2012: DOE Hydrogen: Prices of hydrogen produced by distributed steam methane reforming, as predicted by H2A Production Model from United States Department of Energy, assuming price of natural gas of US$3/MMBtu (US$10/MWh; US$0.10/m 3). Does not include cost of storage and distribution. 1: 2 H (D ...
The Rhind Mathematical Papyrus, [1] [2] an ancient Egyptian mathematical work, includes a mathematical table for converting rational numbers of the form 2/ n into Egyptian fractions (sums of distinct unit fractions ), the form the Egyptians used to write fractional numbers. The text describes the representation of 50 rational numbers.
A simple fraction contains no fraction either in its numerator or its denominator. A fraction is in lowest terms if the only factor common to the numerator and the denominator is 1. An expression which is not in fractional form is an integral expression. An integral expression can always be written in fractional form by giving it the denominator 1.
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