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Rules and style conventions for expressing values of quantities
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Summary
Unit symbols
Unit names
Rules and style conventions for expressing values of quantities

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Related articles
Sections 5.3.2--5.3.6
Section 5.3.7
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SI brochure, Section 5.3


5.3.1 Value and numerical value of a quantity, and the use of quantity calculus

The value of a quantity is expressed as the product of a number and a unit, and the number multiplying the unit is the numerical value of the quantity expressed in that unit. The numerical value of a quantity depends on the choice of unit. Thus the value of a particular quantity is independent of the choice of unit, although the numerical value will be different for different units.

Symbols for quantities are generally single letters set in an italic font, although they may be qualified by further information in subscripts or superscripts or in brackets. Thus C is the recommended symbol for heat capacity, Cm for molar heat capacity, Cm,p for molar heat capacity at constant pressure, and Cm,V for molar heat capacity at constant volume.

Recommended names and symbols for quantities are listed in many standard references, such as the ISO and IEC 80000 series Quantities and units, the IUPAP SUNAMCO Red Book Symbols, Units, Nomenclature and Fundamental Constants in Physics, and the IUPAC Green Book Quantities, Units and Symbols in Physical Chemistry. However, symbols for quantities are recommendations (in contrast to symbols for units, for which the use of the correct form is mandatory). In particular circumstances authors may wish to use a symbol of their own choice for a quantity, for example in order to avoid a conflict arising from the use of the same symbol for two different quantities. In such cases, the meaning of the symbol must be clearly stated. However, neither the name of a quantity, nor the symbol used to denote it, should imply any particular choice of unit.

Symbols for units are treated as mathematical entities. In expressing the value of a quantity as the product of a numerical value and a unit, both the numerical value and the unit may be treated by the ordinary rules of algebra. This procedure is described as the use of quantity calculus, or the algebra of quantities. For example, the equation T = 293 K may equally be written T/K = 293. It is often convenient to write the quotient of a quantity and a unit in this way for the heading of a column in a table, so that the entries in the table are all simply numbers. For example, a table of vapour pressure against temperature, and the natural logarithm of vapour pressure against reciprocal temperature, may be formatted as shown below.

T/K 103 K/T p/MPa ln(p/MPa)
216.55 4.6179 0.5180 –0.6578
273.15 3.6610 3.4853 1.2486
304.19 3.2874 7.3815 1.9990

The axes of a graph may also be labelled in this way, so that the tick marks are labelled only with numbers, as in the graph below.

example graph axes

Algebraically equivalent forms may be used in place of 103 K/T, such as kK/T, or 103 (T/K)–1.

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Related articles

Sections 5.3.2--5.3.6
Section 5.3.7
     

Note: For the official text, please refer to the PDF files available at:
  • http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf (in English) and
  • http://www.bipm.org/utils/common/pdf/si_brochure_8_fr.pdf (in French).
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