Number of entities

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Number of entities


The number of entities, N, is different from a mere number. Whereas a number does not have a unit, a number of entities is composed of the numerical value and the countable entity, with the unit of a count [x]. Unfortunately, the dimensionless unit [x] is not explicitely considered by the SI and IUPAC (Mohr and Philipps 2015). This causes confusion, since then the unit [J] relates without discrimination to both: (1) exergy in the instrumental chamber (the system), and (2) exergy per countable entity (cells, particles, molecules, ions, electrons). The unit [J∙x-­1] clearly indicates exergy per particle or object. The unit [x] is a motive unit.

Abbreviation: N [x]

Reference: Gnaiger 2020 MitoPathways

Stating quantity values being pure numbers (p. 151)

There are also some quantities that cannot be described in terms of the seven base quantities of the SI, but have the nature of a count. Examples are a number of molecules, a number of cellular or biomolecular entities (for example copies of a particular nucleic acid sequence), or degeneracy in quantum mechanics. Counting quantities are also quantities with the associated unit one. The unit one is the neutral element of any system of units – necessary and present automatically. There is no requirement to introduce it formally by decision. Therefore, a formal traceability to the SI can be established through appropriate, validated measurement procedures (Section 2.3.3, p. 136).
As discussed in Section 2.3.3, values of quantities with unit one, are expressed simply as numbers. The unit symbol 1 or unit name “one” are not explicitly shown. SI prefix symbols can neither be attached to the symbol 1 nor to the name “one”, therefore powers of 10 are used to express particularly large or small values.
Quantities that are ratios of quantities of the same kind (for example length ratios and amount fractions) have the option of being expressed with units (m/m, mol/mol) to aid the understanding of the quantity being expressed and also allow the use of SI prefixes, if this is desirable (μm/m, nmol/mol). Quantities relating to counting do not have this option, they are just numbers.
The internationally recognized symbol % (percent) may be used with the SI. When it is used, a space separates the number and the symbol %. The symbol % should be used rather than the name “percent”. In written text, however, the symbol % generally takes the meaning of “parts per hundred”. Phrases such as “percentage by mass”, “percentage by volume”, or “percentage by amount of substance” shall not be used; the extra information on the quantity should instead be conveyed in the description and symbol for the quantity.
The term “ppm”, meaning 10-6 relative value, or 1 part in 106, or parts per million, is also used. This is analogous to the meaning of percent as parts per hundred. The terms “parts per billion” and “parts per trillion” and their respective abbreviations “ppb” and “ppt”, are also used, but their meanings are language dependent. For this reason the abbreviations ppb and ppt should be avoided.
  • Reference: Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0. - »Open Access pdf«


  1. Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0. - »Open Access pdf«
  2. Gnaiger E (2019) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Mitochondr Physiol Network 24.05. Oroboros MiPNet Publications, Innsbruck:112 pp. - »Bioblast link«
  3. Mohr PJ, Phillips WD (2015) Dimensionless units in the SI. Metrologia 52:40-7.


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