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Count

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Count

Description

Count or number of entities, NX, is a quantity containing a defined entity type, X, which is a countable object or event. 'Count' is synonymous with 'number of entities' and is one of the most fundamental quantities in physics, but the name, symbol and unit are not included in the SI as a base quantity or base unit. 'Number of entities' and 'number' are distinguished (German: Anzahl versus Zahl). The dimension of the count, C, is the entity X. The count, therefore, is not a pure dimensionless number. Not all sample types contain countable objects. Countable objects are particles, such as electrons, molecules, packaging units (parcels), cells, organisms, individuals, patients. The magnitude of a count, N, is expressed by a pure number times the counting unit [x]. The name 'counting unit' is proposed for the unit [x]. x ('times') indicates how many times different members of the defined entity are accounted for in a defined system (not how many times the same member of the defined entity is re-counted in the system ā€” consider the political problem of counting votes), or how many times a defined event is counted during a defined period of time. A prefix can be used with the counting unit [x], like with any other symbol of SI units: Mx = 106 x; Āµx = 10-6 x; Gx = 109 x; nx = 10-9 x. If appropriate, it is convenient to write simply 'unit' instead of 'counting unit'. Examples: Avogadro constant, NA, expressed in 'counting units per mole' [xĀ·mol-1]; body mass expressed in 'kilograms per unit' [kgĀ·x-1]; frequency (counts per time, N/t), expressed in 'units per second' (times per second) [xĀ·s-1].

Abbreviation: NX [x]

Reference: Gnaiger 2020 MitoPathways

Communicated by Gnaiger Erich 2019-08-15, last update 2020-05-17

SI and IUPAC

Unfortunately, the counting unit [x] is not explicitly considered by the SI and IUPAC (Mohr and Philipps 2015). This causes confusion, since then the unit 'joule' [J] relates without discrimination to both: (1) exergy of the system (instrumental chamber) or the (sub)sample in the system, and (2) exergy per countable entity (particles, molecules, ions, electrons, cells, packaging units). In contrast, joule per counting unit [Jāˆ™x-Ā­1] clearly indicates exergy per entity. The unit [x] is a motive unit.


Base quantities and number of entities

SI-units-elementary quantities.png
Quantity Symbol for quantity Q Symbol for dimension Name of abstract unit uQ Symbol for unit uQ [*]
elementary entity *,$ UX U elementary unit x
count *,$ NX = NĀ·UX X elementary unit x
amount of substance *,Ā§ nX = NXĀ·NA-1 N mole mol
charge *,ā‚¬ Qel = zXĀ·eĀ·NX IĀ·T coulomb C = AĀ·s
length l L meter m
mass m M kilogram kg
time t T second s
electric current I I ampere A
thermodynamic temperature T Ī˜ kelvin K
luminous intensity Iv J candela cd
[*] SI units, except for the canonical 'elementary unit' [x]. The following footnotes are canonical comments, related to iconic symbols.
* For the elementary quantities NX, nX, and Qel, the entity-type X of the elementary entity UX has to be specified in the text and indicated by a subscript: nO2; Nce; Qel.
$ Count NX equals the number of elementary entities UX. In the SI, the quantity 'count' is explicitly considered as an exception: "Each of the seven base quantities used in the SI is regarded as having its own dimension. .. All other quantities, with the exception of counts, are derived quantities" (Bureau International des Poids et Mesures 2019 The International System of Units (SI)). An elementary entity UX is a material unit, it is not a count (UX is not a number of UX). NX has the dimension X of a count and UX has the dimension U of an elementary entity; both quantities have the same abstract unit, the 'elementary unit' [x].
Ā§ Amount nX is an elementary quantity, converting the elementary unit [x] into the SI base unit mole [mol] using the Avogadro constant NA.
ā‚¬ Charge is a derived SI quantity. Charge is an elementary quantity, converting the elementary unit [x] into coulombs [C] using the elementary charge e, or converting moles [mol] into coulombs [C] using the Faraday constant F. zX is the charge number per elementary entity UX, which is a constant for any defined elementary entity UX. Qel = zXĀ·FĀ·nX
SI-units.png

Stating quantity values being pure numbers (p. 151)

Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0. - Ā»Open Access pdfĀ«
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 ā€“ 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 ā€œoneā€ are not explicitly shown. SI prefix symbols can neither be attached to the symbol 1 nor to the name ā€œoneā€, 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 (Ī¼m/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 ā€œpercentā€. In written text, however, the symbol % generally takes the meaning of ā€œparts per hundredā€. Phrases such as ā€œpercentage by massā€, ā€œpercentage by volumeā€, or ā€œpercentage by amount of substanceā€ shall not be used; the extra information on the quantity should instead be conveyed in the description and symbol for the quantity.
The term ā€œppmā€, 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 ā€œparts per billionā€ and ā€œparts per trillionā€ and their respective abbreviations ā€œppbā€ and ā€œpptā€, are also used, but their meanings are language dependent. For this reason the abbreviations ppb and ppt should be avoided.


References

 YearReference
Gnaiger 2020 MitoFit x2021Gnaiger E (2021) The elementary unit ā€” canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. https://doi.org/10.26124/mitofit:200004.v2
Gnaiger 2020 BEC MitoPathways2020Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. https://doi.org/10.26124/bec:2020-0002
BEC 2020.1 doi10.26124bec2020-0001.v12020Gnaiger E et al ā€• MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. https://doi.org/10.26124/bec:2020-0001.v1
Bureau International des Poids et Mesures 2019 The International System of Units (SI)2019Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216. ISBN 978-92-822-2272-0
Mohr 2015 Metrologia2015Mohr Peter J, Phillips William D (2015) Dimensionless units in the SI. Metrologia 52:40-7.
Cohen 2008 IUPAC Green Book2008Cohen ER, Cvitas T, Frey JG, Holmstrƶm B, Kuchitsu K, Marquardt R, Mills I, Pavese F, Quack M, Stohner J, Strauss HL, Takami M, Thor HL (2008) Quantities, Units and Symbols in Physical Chemistry. IUPAC Green Book 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge.
Baroody 1983 J Research in Mathematics Education1983Baroody AJ, Price J (1983) The development of numberā€“word sequence in the counting of three-year-olds. J Research in Mathematics Education 14:361-8.


SI-units.png


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Entity, count, and number, and SI base quantities / SI base units
SI-units.png
Quantity name Symbol Unit name Symbol Comment
elementary UX elementary unit [x] UX, UB; [x] not in SI
count NX elementary unit [x] NX, NB; [x] not in SI
number N - dimensionless = NXĀ·UX-1
amount of substance nB mole [mol] nX, nB
electric current I ampere [A] A = CĀ·s-1
time t second [s]
length l meter [m] SI: metre
mass m kilogram [kg]
thermodynamic temperature T kelvin [K]
luminous intensity IV candela [cd]
Fundamental relationships
Ā» Avogadro constant NA
Ā» Boltzmann constant k
Ā» elementary charge e
Ā» Faraday constant F
Ā» gas constant R
Ā» electrochemical constant f
SI and related concepts
Ā» International System of Units
Ā» elementary unit x
Ā» SI prefixes
Ā» International Union of Pure and Applied Chemistry, IUPAC
Ā» entity
Ā» quantity
Ā» dimension
Ā» format
Ā» motive unit
Ā» iconic symbols



MitoPedia concepts: Ergodynamics