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In order to convert a rational number represented as a fraction into decimal form, one may use long division. For example, consider the rational number 5 / 74 : 0.0 675 74 ) 5.00000 4.44 560 518 420 370 500 etc. Observe that at each step we have a remainder; the successive remainders displayed above are 56, 42, 50.
This sequence takes a particularly simple form for prime k: 2 ⋅ 2 k − 1 − 1 / k . For example: 2 ⋅ 2 13 − 1 − 1 / 13 = 630 is the number of cycles of length 13. Since this case of the logistic map is chaotic for almost all initial conditions, all of these finite-length cycles are unstable.
Examples include: = 0. 142857 and 142 + 857 = 999. = 0. 01369863 and 0136 + 9863 = 9999. E. Midy proved a general result about such fractions, now called Midy's theorem, in 1836. The publication was obscure, and it is unclear whether his proof directly involved 0.999..., but at least one modern proof by William G. Leavitt does.
A stable binary hydride and the simplest pnictogen hydride, ammonia is a colourless gas with a distinctive pungent smell. Biologically, it is a common nitrogenous waste , and it contributes significantly to the nutritional needs of terrestrial organisms by serving as a precursor to fertilisers . [ 13 ]
Nuclear fusion is a reaction in which two or more atomic nuclei (for example, nuclei of hydrogen isotopes deuterium and tritium), combine to form one or more atomic nuclei and neutrons. The difference in mass between the reactants and products is manifested as either the release or absorption of energy .
The fraction of 3 He in helium separated from natural gas in the U.S. was found to range from 70 to 242 parts per billion. [ 22 ] [ 23 ] Hence the US 2002 stockpile of 1 billion normal m 3 [ 21 ] would have contained about 12 to 43 kilograms (26 to 95 lb) of helium-3.