ISO 31-0
ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the SI. It is intended for use in all fields of science and technology and is augmented by more specialized conventions defined in other parts of the ISO 31 standard.
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Quantities and units
ISO 31 covers only physical quantities used for the quantitative description of physical phenomena. It does not cover conventional scales (e.g., Beaufort scale, Richter scale, colour intensity scales), results of conventional tests, currencies, or information content. The presentation here is only a brief summary of some of the detailed guidelines and examples given in the standard.
Physical quantities can be grouped into mutually comparable categories. For example, length, width, diameter and wavelength are all in the same category, that is they are all quantities of the same kind. One particular example of such a quantity can be chosen as a reference quantity, called the unit, and then all other quantities in the same category can be expressed in terms of this unit, multiplied by a number called the numerical value. For example, if we write
- the wavelength is λ = 6.982 × 10−7 m
then "λ" is the symbol for the physical quantity (wavelength), "m" is the symbol for the unit (metre), and "6.982 × 10−7" is the numerical value of the wavelength in metres.
More generally, we can write
- A = {A} · [A]
where A is the symbol for the quantity and {A} symbolizes the numerical value of A if it is expressed using the unit [A]. Both the numerical value and the unit symbol are factors and their product is the quantity.
The value of a quantity is independent of the unit chosen to represent it. It must be distinguished from the numerical value of the quantity that occurs when the quantity is expressed in a particular unit. The above curly-bracket notation could be extended with a unit-symbol index to clarify this dependency, as in {λ}m = 6.982 × 10−7 or equivalently {λ}nm = 698.2. In practice, where it is necessary to refer to the numerical value of a quantity expressed in a particular unit, it is notationally more convenient to simply divide the quantity through that unit, as in
- λ/m = 6.982 × 10−7
or equivalently
- λ/nm = 698.2.
This is a particularly useful and widely used notation for labeling the axes of graphs or for the headings of table columns, where repeating the unit after each numerical value can be typographically inconvenient.
Typographic conventions
Symbols for quantities
- Quantities are generally represented by a symbol formed from single letters of the Latin or Greek alphabet.
- Symbols for quantities are set in italic type, independent of the type used in the rest of the text.
- If in a text different quantities use the same letter symbol, they can be distinguished via subscripts.
- A subscript is only set in italic type if it consists of a symbol for a quantity or a variable. Other subscripts are set in upright (roman) type. For example, write Vn for a "nominal volume" (where "n" is just an abbreviation for the word "nominal"), but write Vn if n is a running index number.
Names and symbols for units
- If an internationally standardized symbol exists for a unit, then only that symbol should be used. See the SI article for the list of standard symbols defined by the International System of Units. Note that the distinction between uppercase and lowercase letters is significant for SI unit symbols. For example, "k" is the prefix kilo and "K" stands for the unit kelvin. The symbols of all SI units named after a person start with an uppercase letter, as do the symbols of all prefixes from mega on upwards. All other symbols are lowercase, with litre being the only special case.
- Symbols for units should be printed in an upright (roman) typeface.
Numbers
- Numbers should be printed in upright (roman) type.
- Numbers consisting of long sequences of digits can be made more readable by separating them into groups, preferably groups of three, separated by a small space. ISO 31-0 specifies that such groups of digits should never be separated by a comma or point, as these are reserved for use as the decimal sign.
- ISO 31-0 specifies that the decimal sign is the comma on the baseline, but recognizes that in English documents a dot on the line is also commonly used.
- For numbers whose magnitude is less than 1, the decimal sign should be preceded by a zero.
Expressions
- Unit symbols follow the numerical value in the expression of a quantity.
- Numerical value and unit symbol are separated by a space. This rule also applies to the symbol "°C" for degrees celsius, as in "25 °C". The only exception are the symbols for the units of plane angle degree, minute and second, which follow the numerical value with a space inbetween (for example "30°").
- Where quantities are added or subtracted, parenthesis can be used to distribute a unit symbol over several numerical values, as in
- T = 25 °C − 3 °C = (25 − 3) °C
- P = 100 kW ± 5 kW = (100 ± 5) kW
- (but not: 100 ± 5 kW)
- d = 12 × (1 ± 10−4) m
Mathematical signs and symbols
A comprehensive list of internationally standardized mathematical symbols and notations can be found in ISO 31-11.