FractionA fraction (from fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: and ) consists of an integer numerator, displayed above a line (or before a slash like ), and a non-zero integer denominator, displayed below (or after) that line.
Nitrogen cycleThe nitrogen cycle is the biogeochemical cycle by which nitrogen is converted into multiple chemical forms as it circulates among atmospheric, terrestrial, and marine ecosystems. The conversion of nitrogen can be carried out through both biological and physical processes. Important processes in the nitrogen cycle include fixation, ammonification, nitrification, and denitrification. The majority of Earth's atmosphere (78%) is atmospheric nitrogen, making it the largest source of nitrogen.
Nitrogen fixationNitrogen fixation is a chemical process by which molecular nitrogen (N2), which has a strong triple covalent bond, is converted into ammonia (NH3) or related nitrogenous compounds, typically in soil or aquatic systems but also in industry. The nitrogen in air is molecular dinitrogen, a relatively nonreactive molecule that is metabolically useless to all but a few microorganisms. Biological nitrogen fixation or diazotrophy is an important microbe-mediated process that converts dinitrogen (N2) gas to ammonia (NH3) using the nitrogenase protein complex (Nif).
Egyptian fractionAn Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction above sums to . Every positive rational number can be represented by an Egyptian fraction.
Continued fractionIn mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on. In a finite continued fraction (or terminated continued fraction), the iteration/recursion is terminated after finitely many steps by using an integer in lieu of another continued fraction. In contrast, an infinite continued fraction is an infinite expression.
FertilizerA fertilizer (American English) or fertiliser (British English) is any material of natural or synthetic origin that is applied to soil or to plant tissues to supply plant nutrients. Fertilizers may be distinct from liming materials or other non-nutrient soil amendments. Many sources of fertilizer exist, both natural and industrially produced. For most modern agricultural practices, fertilization focuses on three main macro nutrients: nitrogen (N), phosphorus (P), and potassium (K) with occasional addition of supplements like rock flour for micronutrients.
Trichloroacetic acidTrichloroacetic acid (TCA; TCAA; also known as trichloroethanoic acid) is an analogue of acetic acid in which the three hydrogen atoms of the methyl group have all been replaced by chlorine atoms. Salts and esters of trichloroacetic acid are called trichloroacetates. It is prepared by the reaction of chlorine with acetic acid in the presence of a suitable catalyst such as red phosphorus. This reaction is Hell–Volhard–Zelinsky halogenation. CH3COOH + 3 Cl2 → CCl3COOH + 3 HCl Another route to trichloroacetic acid is the oxidation of trichloroacetaldehyde.
Chloroacetic acidChloroacetic acid, industrially known as monochloroacetic acid (MCA), is the organochlorine compound with the formula ClCH2CO2H. This carboxylic acid is a useful building block in organic synthesis. It is a colorless solid. Related compounds are dichloroacetic acid and trichloroacetic acid. Chloroacetic acid was first prepared (in impure form) by the French chemist Félix LeBlanc (1813–1886) in 1843 by chlorinating acetic acid in the presence of sunlight, and in 1857 (in pure form) by the German chemist Reinhold Hoffmann (1831–1919) by refluxing glacial acetic acid in the presence of chlorine and sunlight, and then by the French chemist Charles Adolphe Wurtz by hydrolysis of chloroacetyl chloride (ClCH2COCl), also in 1857.
HydrolysisHydrolysis (haɪˈdrɒlɪsɪs; ) is any chemical reaction in which a molecule of water breaks one or more chemical bonds. The term is used broadly for substitution, elimination, and solvation reactions in which water is the nucleophile. Biological hydrolysis is the cleavage of biomolecules where a water molecule is consumed to effect the separation of a larger molecule into component parts. When a carbohydrate is broken into its component sugar molecules by hydrolysis (e.g.
Unit fractionA unit fraction is a positive fraction with one as its numerator, 1/n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number. Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc. When an object is divided into equal parts, each part is a unit fraction of the whole. Multiplying two unit fractions produces another unit fraction, but other arithmetic operations do not preserve unit fractions.
