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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, 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.
But, in concept, there is no problem adding quantities of the same dimension expressed in different units. For example, 1 metre added to 1 foot is a length, but one cannot derive that length by simply adding 1 and 1. A conversion factor, which is a ratio of like-dimensioned quantities and is equal to the dimensionless unity, is needed:
For example, if "x" represented mass, the letter "m" might be an appropriate symbol to represent the dimensionless mass quantity. In this article, the following conventions have been used: t – represents the independent variable – usually a time quantity.
Dimensionless quantities of chemistry (4 P) Countable quantities (1 C, 4 P) Pages in category "Dimensionless quantities" The following 9 pages are in this category ...
Since the kernel is only defined to within a multiplicative constant, if the above dimensionless constant is raised to any arbitrary power, it will yield another equivalent dimensionless constant. In this example, three of the four dimensional quantities are fundamental units, so the last (which is ) must be a combination of the previous.
Dimensionless quantities (2 C, 9 P) R. Ratios (11 C, 59 P) T. Dimensionless numbers of thermodynamics (21 P) U. Dimensionless units (1 C, 4 P) Pages in category ...
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