Quantity symbols, values and numerical values
Quantities characterize objects, substances, different phenomena and processes in our surroundings.
For that reason, the quantity can be defined as a property of a phenomena, body or substance that
can be expressed with a number and a reference. [1] Reference can be a measurement unit, a
measurement procedure, a reference substance or a combination of those.
Depending on the type of reference, the quantitative expression of a quantity, i.e. the value can be
product of
• The measurement unit and the number (the measurement unit 1 is not shown when the
dimension of the quantity is one), or
• The number and the reference to the applied measurement procedure, for example Rockwell
C hardness (load 150 kg) 41,5 HRC (150 kg) of the surface of the sample, or
• The number and reference to used reference substance, for example concentration of lutropin
in a given sample of human blood plasma (WHO International Standard 80/552 used as a
calibrator) 5,5 IU/l, where IU stands for “WHO International Unit”, l stands for liter.
Quantity Q value is determined with following relation Q = {Q}∩[Q], where {Q} is a numerical
value that is chosen regarding to reference, ∩ sign of common share of elements {Q} and [Q] and
[Q] is chosen reference. Changing the reference [Q] automatically leads to the change in the
numerical value {Q} according to relation above. If reference should be a measurement unit then in
previous relation the common share stands for multiplication and ∩ will be replaced with
multiplication sign „·“ Therefore quantity value Q can be expressed with relation, Q = {Q}·[Q].
For example when quantity values are presented as 2,5 kg, 1,2 m 1 090 hPa, 15000$, 3,2 %, 98 °C
etc. then the numbers presented in the values are numerical values, that are quotient of quantity
values and used units of reference. Therefore, it is recommended that in headers of the tables that
contain numerical values (numbers), a quantity symbol should be divided with unit as shown in Table
1. In table headers, it is incorrect to present quantity unit after symbol separated by comma or in the
square brackets.
Table 1
Sample
Square bar
Round bar
Material
Steel
Aluminum
Length
l/m
0,51
1,28
Mass
m/kg
2,32
1,98
Material density
ρ/(kg/m3)
7 800
2 699
Quantity, whose value cannot be presented as a multiplication of number and unit, can be
characterized with a reference scale, a description of measurement procedure or both. Therefore,
the numerical value is a number in the relation to quantity value, which does not have a reference.
For example, in case of relative part 4 mmol/mol the numerical value is 4 and reference unit is
mmol/mol. The unit mmol/mol is numerically 0,001, but this number is not a part of the numerical
value of quantity value that is constantly 4. Another simple example is given as 2,4 kg: in this
quantity value numerical, the value is {m} = (2,4 kg)/kg = 2,4. On the other hand, in case of
quantity value 2 400 g, the numerical value is {m} = (2 400 g)/g = 2 400. The numerical values
should be presented at graphs analogously. For example, in figure 1 where measurement results
of temperature and pressure change of two different objects are presented graphically. The dotted
lines on figure 1 represent the range of the relations, which are limited with expanded uncertainty
(probability level 95 %). In this range, the line acquired by experiment can have arbitrary
positions, which are all correct at probability level 95 %. However, the relation acquired for first
object (left on figure 1) shows that suggested (and computed) pressure and temperature relation
is probably not linear, because five measurement results are outside of range limited with
expanded uncertainty.
1
Figure 1
International standard [3] recommends that in case of numerical values with many digits the
numerical values (numbers) should be grouped by three based on the decimal comma. Groups are
separated by space. This is used when before or after comma there are more than four digits.
However, this suggestion cannot be used for describing monetary values because of the possibility
to fill spaces with extra numbers. Even though USA and England have adopted mentioned
international standard, some of technical and science journals editors in those two countries still
use traditionally a dot as a decimal separator and comma instead of space. This writing style of
numerical values should be given up.
Symbols of the quantity should be written in the Latin and Greek alphabet using capital or small
letters. The symbols usually contain indexes for distinguishing purpose. Indexes can refer to
objects, which are not quantities. The symbols are always consisted of one letter and are written
in italic regardless of the text type or font.
There is no dot used at the end of symbol of quantity except at the end of the sentence. The
indexes are used in the symbols of the quantity to distinguish between different values of the same
quantity and to define for what purpose the quantity is used. The indexes of the symbols of the
quantities, which refer to physical, chemical and biological quantities, mathematical variables or
running number, are written and presented always in italic. Other indexes of the symbols that
refer to some word or fixed sequence number are written and presented by normal characters.
Examples about writing some symbol’s indexes are presented in table 2 and in the brackets are
shown the reasoning of the writing style.
Table 2
Italic
Cp (p − pressure)
xi (i − symbol of running number)
Σnanωn (n − symbol of running number)
Fx (x – force’s component along the x-axis)
yij (i,j – symbols for running numbers)
Iλ (λ − wavelength)
Normal characters
Cg (g − gas)
x2 (2 − second)
gn (n − normal, standard)
µr (r – relative)
Sm (m – molar)
T1/2 (1/2 – half)
Literature:
[1] Rein Laaneots, Olev Mathiesen, Jürgen Riim. Metroloogia. Textbook for universities //
Tallinn: TTÜ kirjastus, 2012.
[2] ISO 80000-1:2009. Quantities and units − Part 1: General. Geneva: ISO, 2009.
Correction ISO 80000-1:2009/Cor 1:2011 // Geneva: ISO, 2011.
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