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ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the SI. It is intended for use in all fields of science and technology and is augmented by more specialized conventions defined in other parts of the ISO 31 standard. It is superseded by ISO 80000-1.
ISO 31 covers only physical quantities used for the quantitative description of physical phenomena. It does not cover conventional scales (e.g., Beaufort scale, Richter scale, colour intensity scales), results of conventional tests, currencies, or information content. The presentation here is only a brief summary of some of the detailed guidelines and examples given in the standard.
Physical quantities can be grouped into mutually comparable categories. For example, length, width, diameter and wavelength are all in the same category, that is they are all quantities of the same kind. One particular example of such a quantity can be chosen as a reference quantity, called the unit, and then all other quantities in the same category can be expressed in terms of this unit, multiplied by a number called the numerical value. For example, if we write
then "λ" is the symbol for the physical quantity (wavelength), "m" is the symbol for the unit (metre), and "6.982 × 10^{−7}" is the numerical value of the wavelength in metres.
More generally, we can write
where A is the symbol for the quantity, {A} symbolizes the numerical value of A, and [A] represents the corresponding unit in which A is expressed here. Both the numerical value and the unit symbol are factors, and their product is the quantity. A quantity itself has no inherent particular numerical value or unit; as with any product, there are many different combinations of numerical value and unit that lead to the same quantity (e.g., A = 300 · m = 0.3 · km = ...). This ambiguity makes the {A} and [A] notations useless, unless they are used together.
The value of a quantity is independent of the unit chosen to represent it. It must be distinguished from the numerical value of the quantity that occurs when the quantity is expressed in a particular unit. The above curly-bracket notation could be extended with a unit-symbol index to clarify this dependency, as in {λ}_{m} = 6.982 × 10^{−7} or equivalently {λ}_{nm} = 698.2. In practice, where it is necessary to refer to the numerical value of a quantity expressed in a particular unit, it is notationally more convenient to simply divide the quantity through that unit, as in
or equivalently
This is a particularly useful and widely used notation for labelling the axes of graphs or for the headings of table columns, where repeating the unit after each numerical value can be typographically inconvenient.
See Sect. 3.3 of the Standard text.
A comprehensive list of internationally standardized mathematical symbols and notations can be found in ISO 31-11.
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