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This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers , dimensionless ratios, or dimensionless physical constants ; these topics are discussed in the article.
Dimensionless quantities can be obtained as ratios of quantities that are not dimensionless, but whose dimensions cancel out in the mathematical operation. [19] [20] Examples of quotients of dimension one include calculating slopes or some unit conversion factors.
Dimensionless quantities (2 C, 9 P) R. Ratios (11 C, 58 P) T. ... Pages in category "Dimensionless numbers" The following 57 pages are in this category, out of 57 total.
Dimensionless quantities, or quantities of dimension one, [2] are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. [ 3 ] [ 4 ] Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units .
Parts-per notations are all dimensionless quantities: in mathematical expressions, the units of measurement always cancel. In fractions like "2 nanometers per meter" (2 n m / m = 2 nano = 2×10 −9 = 2 ppb = 2 × 0.000 000 001 ), so the quotients are pure-number coefficients with positive values less than or equal to 1.
For example, if x is a quantity, then x c is the characteristic unit used to scale it. As an illustrative example, consider a first order differential equation with constant coefficients: + = (). In this equation the independent variable here is t, and the dependent variable is x.
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