(Redirected from Number of entities)

## Description

Count NX is a quantity containing a number of defined elementary entities X. The single elementary entity X is a countable object or event. NX is the number of X, whereas X is the single entity. 'Count' is synonymous with 'number of entities' (number of particles such as molecules, or objects such as cells). Count is one of the most fundamental quantities from physics to biology. In the International System of Units (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)). Count is not included in the SI as a base quantity. Since 2019-05-20, the amount of substance, n, of a system is defined as "a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles" (Bureau International des Poids et Mesures 2019). The quantity 'amount', n, therefore, is a number of specified elementary entities expressed in the unit 'mole' [mol] with dimension N. Logically, the quantities 'amount' and 'count' have exactly identical meanings, since the quantity 'count', N, is a number of specified elementary entities expressed in the unit 'counting unit' [x] with dimension X. Similarly, charge is a derived SI unit with dimension A·T, converting the counting unit [x] into coulombs [C] using the elementary charge.

'Count' (number of entities) and 'number' are distinguished (German: Anzahl versus Zahl). A count is a quantity (italic font symbol, N) represented by a number and the corresponding entity X (cell count: Nce). In contrast, a number is represented by numerals only, is a mathematical object used for counting and measuring, and is thus not a physicochemical quantity. Neither is a defined elementary entity X a count, it is rather the dimension of a count (entity type: cell, ce). Not all sample types contain countable objects. Countable objects are physicochemical particles (atoms, electrons, ions, molecules), ensembles (packaging units, parcels), biological entities (cells, organisms, individuals, patients), and units of transmitted information. The magnitude of a count, N, is expressed by a 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 — 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], applying the same convention for any symbol of SI units: Mx = 106 x; µx = 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' [x·mol-1]; elementary charge, e, expressed in 'coulombs per counting unit' [C·x-1]; body mass is mass per single body (not mass of several bodies) expressed in 'kilograms per unit' [kg·x-1]; frequency (counts per time, N/t), expressed in 'units per second' (times per second) [x·s-1].

Abbreviation: NX [x]

## Contents

```Communicated by Gnaiger Erich 2019-08-15, last update 2020-05-20
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## Base quantities and count

Base quantity Symbol for quantity Symbol for dimension Name of SI unit Symbol for SI unit [*]
length l L meter m
mass m M kilogram kg
time t T second s
electric current I I ampere A
thermodynamic temperature T Θ kelvin K
amount of substance *,§ n = N·NA-1 N mole mol
count *,\$ N X counting unit x
charge *,€ Q = N·e = n·F I·T coulomb C = A·s
luminous intensity Iv J candela cd
[*] »SI base units
* For the quantities n, N and Q, the entity X has to be specified in the text or indicated by a subscript or in parentheses: nX; NX; QX.
§ 'Amount is a counting quantity, converting the counting unit [x] into moles [mol] using the Avogadro constant, NA.
\$ 'Count' is synonymous with 'number of counting entities'. 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)).
Charge is a derived SI quantity, included here for comparison. Charge is a counting quantity, converting the counting unit [x] into coulombs [C] using the elementary charge, e, or converting moles [mol] into coulombs [C] using the Faraday constant, F.

## 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, for example, the unit 'joule' [J] relates without discrimination to both: (1) exergy per elementary entity, and (2) exergy of the system (instrumental chamber) or the (sub)sample in the system. In contrast, joule per counting unit [J∙x-­1] clearly indicates exergy per entity. The unit [x] is a motive unit.

## 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. - »Open Access pdf«
```
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.