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9 Numbers, quantities, units and values

9.1 Representation of numbers and numerical values

  • Numbers should be written in upright type, irrespective of the type used in the rest of the text.
  • The decimal sign shall be a comma on the line in all language versions.
  • If the magnitude (absolute value) of a number less than 1 is written in decimal form, the decimal sign shall be preceded by a zero.

EXAMPLE 1     0,001

  • Each group of three digits shall be separated by a small space from the preceding digits, counting from the decimal sign. This also applies to digits following the decimal sign. When there is no decimal sign, the counting shall be from the rightmost digit towards the left. The separation into groups of three digits does not apply to binary and hexadecimal numbers, numbers designating years or the numbering of standards.

EXAMPLE 2     23 456          2 345           2,345 6         2,345 67  but the year 2011

  • When numbers or numerical values have a decimal separator, their multiplication shall be indicated by the multiplication cross (×), instead of a half-high dot.

EXAMPLE 3       2 . m
EXAMPLE 4       1,7 × h

  • ISO 80000-2 gives an overview of multiplication symbols for numbers.

 

9.2 Representation of numbers, symbols for variable quantities and numerical values for programming languages, pseudo-code and mark-up languages

Where the document defines, describes, refers to or contains programming language, pseudo-code or mark-up language text, the representation of the numbers, symbols for variable quantities and numerical values shall follow the syntax of the appropriate programming language, pseudo-code or mark-up language.

 

9.3 Quantities, units, symbols and signs

9.3.1 Quantities

  • Quantity symbols should be written in italic type, irrespective of the type used in the rest of the text.
  • Quantity symbols shall be chosen, wherever possible, from the various parts of the IEC 60027 series, the ISO 80000 series, the IEC 80000 series and ISO Guide 99.
  • Subscripts for quantity symbols are allowed and are printed in italic type when they represent a quantity or a mathematical variable. They are printed in upright type when they represent a word or a fixed number.


EXAMPLE 1

Italic subscripts

Cp     (p: pressure)

C𝒾     (𝒾: running number)

 

Roman subscripts

Cg     (g: gas)

C3     (3: third)

 

 

The symbol of the product of two or more quantities is indicated in one of the following ways:

ab, a b, a · b, a × b, a * b

abc, a b c, a · b · c, a × b × c, a * b * c

The multiplication cross (×) may also be used to indicate vector products or cartesian products.

 

EXAMPLE 2      

 

The half-high dot (·) may also be used to indicate a scalar product of vectors and comparable cases, and may also be used to indicate a product of scalars and in compound units.

 

EXAMPLE 3       U = R · I
EXAMPLE 4       rad · m2/kg

 

 

The division of one quantity by another is indicated in one of the following ways:

 

A solidus (/) shall not be followed by a multiplication sign or a division sign on the same line unless parentheses are inserted to avoid any ambiguity:

(a / b) / c = a / (bc), not a / b / c

 

Names of quantities or multiletter abbreviated terms, for example, presented in italics or with subscripts, shall not be used in the place of symbols.

 

EXAMPLE 5       Write ρ = m / V and not density = mass / volume.

 

9.3.2 Units

  • The International System of units (SI) as set out in the ISO 80000 series and the IEC 80000 series shall be used.
  • The units in which any values are expressed shall be indicated.
  • It is not permitted to modify a unit symbol (e.g. by means of a subscript) to give information about the special nature of the quantity or context of measurement.

 

EXAMPLE 1 

Correct: Umax= 500 V

Incorrect: U = 500 Vmax

 

Language-specific abbreviated terms such as "ppm" should not be used, if possible. If it is necessary to use language-specific abbreviated terms such as "ppm", their meaning shall be explained.

 

Mathematical signs and symbols shall be in accordance with ISO 80000-2.

 

Use Annex B as a checklist of the quantities and units that shall be used.

 

 

9.4 Values, intervals and tolerances

9.4.1 General

 

To express values of physical quantities, Arabic numerals (called "numerical values") followed by the international symbol for the unit shall be used (see the ISO 80000 series, the IEC 80000 series, the IEC 60027 series and ISO/IEC Guide 99).

 

EXAMPLE 1       80 mm × 25 mm × 50 mm (not 80 × 25 × 50 mm)

 

In the expression of a quantity value, there is always a space between the numerical value and the unit symbol. The only exception to this convention is for plane angles expressed with superscript-type unit symbols. However, the degree should preferably be subdivided decimally. In some fields of science, the usage of the units minute (ʹ) and second (ʺ) is preferred, e.g. for geographic coordinates.

 

EXAMPLE 2       θ = 1 rad = 57,295 8° instead of θ = 1 rad = 57°17ʹ45ʺ
EXAMPLE 3       60°10ʹ15ʺN 24°56ʹ15ʺE (the position of Helsinki, Finland)

 

The quantity value is expressed with only one symbol unit, with the exception of sexagesimally divided units like the plane angle (in special fields like astronomy, cartography and navigation) and the time, although the seconds are decimally divided.

 

EXAMPLE 4      L = 1,234 m but ∇t = 10 h 31 min 19,93 s

 

To designate a set of values between a and b, where a < b, the symbol [a, b] is used, designated by "interval". The difference r = ba, denoted r[a,b], is designated by "the range of the interval [a, b]".

 

EXAMPLE 5      The two end points 78 μF and 82 μF of the interval [78, 82] μF, also denoted [78 μF, 82 μF], can be stated as 80 μF ± 2 μF or (80 ± 2) μF, although this expression is often used erroneously to denote the interval preferably denoted using brackets like [80 μF ± 2 μF], [(80 ± 2) μF] or even [80 ± 2] μF.

 

EXAMPLE 6      Consequently, λ = 220 × (1 ± 0,02) W/(m · K) denotes the two end points λ1 = 220 × 0,98 W/(m · K) and λ2 = 220 × 1,02 W/(m · K).

 

EXAMPLE 7      10 kPa to 12 kPa (not 10 to 12 kPa or 10 – 12 kPa) is another way to denote the [10, 12] kPa interval.

 

EXAMPLE 8      0 °C to 10 °C (not 0 to 10 °C or 0 – 10 °C) is another way to denote the [0, 10] °C interval.

 

To indicate that one of the end points is excluded from the interval, the square bracket may be replaced by a parenthesis.

 

EXAMPLE 9      x ∈ [a, b] expresses a ≤ x ≤ b, while [a, b) expresses a ≤ x < b and (a, b] expresses a < x ≤ b.

 

Values and dimensions shall be indicated as either nominal, ordinal, theoretically exact, or including a tolerance.

 

By the same token, their tolerances (if applicable) shall be specified in an unambiguous manner.

 

EXAMPLE 10 
EXAMPLE 11 

 

In order to avoid misunderstanding, tolerances on values expressed in per cent shall be expressed in a mathematically correct form.

 

EXAMPLE 12      Write "from 63 % to 67 %" to express a range.
EXAMPLE 13      Write "(65 ± 2) %" to express a centre value with a tolerance.

 

Any value or dimension that is mentioned for information only shall be clearly distinguishable from requirements.

 

9.4.2 Limiting values

 

For some purposes, it is necessary to specify limiting values (maximum, minimum). Usually one limiting value is specified for each characteristic. In the case of several widely used categories or levels, several limiting values are required.

 

 

Limiting values of strictly local importance shall not be included in a document.

 

9.4.3 Selected values

 

For some purposes, values or series of values may be selected, particularly for variety control and interface purposes. They may be selected in accordance with the series of preferred numbers given in ISO 3 (see also ISO 17 and ISO 497), or according to some modular system or other determining factors. For the electrotechnical field, recommended systems of dimensional sizes are given in IEC Guide 103.

 

Documents that have been established to specify selected values for equipment, or components that may be referred to in the provisions of other documents, shall be regarded, in this respect, as basic standards.

 

EXAMPLE 1  For electrotechnical work, IEC 60063 specifies series of preferred values for resistors and capacitors.
EXAMPLE 2   For chemical testing, ISO/TC 48 has developed standards for laboratory equipment.

 

Values of strictly local importance shall not be included in a document. In standardizing a rationalized series of values, existing series shall be examined to see whether any would be acceptable for international application.

 

If a series of preferred numbers is used, difficulties can arise if fractions such as "3,15" are introduced: these can sometimes be inconvenient or require unnecessarily high accuracy. In such cases, they should be rounded in accordance with ISO 497. The specification of different values for use in different countries (whereby both the precise value and the rounded value are contained in the document) shall be avoided.