ISO 31-0
Encyclopedia
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.
, 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.
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
where A is the symbol for the quantity, {A} symbolizes the numerical value of A, and [A] represents the corresponding unit in which A is expressed here. Both the numerical value and the unit symbol are factors, and their product is the quantity. A quantity itself has no inherent particular numerical value or unit; as with any product, there are many different combinations of numerical value and unit that lead to the same quantity (e.g., A = 300 · m = 0.3 · km = ...). This ambiguity makes the {A} and [A] notations useless, unless they are used together.
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
or equivalently
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.
.
International Organization for Standardization
The International Organization for Standardization , widely known as ISO, is an international standard-setting body composed of representatives from various national standards organizations. Founded on February 23, 1947, the organization promulgates worldwide proprietary, industrial and commercial...
ISO 31
ISO 31
International Standard ISO 31 was the most widely respected style guide for the use of physical quantities and units of measurement, and formulas involving them, in scientific and educational documents worldwide...
on quantities
Physical quantity
A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.-Definition of a physical quantity:Formally, the International Vocabulary of Metrology, 3rd edition defines quantity as:...
and units. It provides guidelines for using physical quantities, quantity and unit symbols, and coherent unit systems, especially the SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
. 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
ISO 31
International Standard ISO 31 was the most widely respected style guide for the use of physical quantities and units of measurement, and formulas involving them, in scientific and educational documents worldwide...
standard.
Scope
ISO 31 covers only physical quantities used for the quantitative description of physical phenomena. It does not cover conventional scales (e.g., Beaufort scaleBeaufort scale
The Beaufort Scale is an empirical measure that relates wind speed to observed conditions at sea or on land. Its full name is the Beaufort Wind Force Scale.-History:...
, 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.
Quantities and units
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, {A} symbolizes the numerical value of A, and [A] represents the corresponding unit in which A is expressed here. Both the numerical value and the unit symbol are factors, and their product is the quantity. A quantity itself has no inherent particular numerical value or unit; as with any product, there are many different combinations of numerical value and unit that lead to the same quantity (e.g., A = 300 · m = 0.3 · km = ...). This ambiguity makes the {A} and [A] notations useless, unless they are used together.
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.
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 typeItalic typeIn typography, italic type is a cursive typeface based on a stylized form of calligraphic handwriting. Owing to the influence from calligraphy, such typefaces often slant slightly to the right. Different glyph shapes from roman type are also usually used—another influence from calligraphy...
, 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 (romanRoman typeIn typography, roman is one of the three main kinds of historical type, alongside blackletter and italic. Roman type was modelled from a European scribal manuscript style of the 1400s, based on the pairing of inscriptional capitals used in ancient Rome with Carolingian minuscules developed in the...
) 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 SISiSi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
articles 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 or a place start with an uppercase letter, as do the symbols of all prefixes from mega on upwards. All other symbols are lowercase; the only exception is litreLitrepic|200px|right|thumb|One litre is equivalent to this cubeEach side is 10 cm1 litre water = 1 kilogram water The litre is a metric system unit of volume equal to 1 cubic decimetre , to 1,000 cubic centimetres , and to 1/1,000 cubic metre...
, where both l and L are allowed. However, it is stated that the CIPM will examine whether one of the two may be suppressed.
- Symbols for units should be printed in an upright (romanRoman typeIn typography, roman is one of the three main kinds of historical type, alongside blackletter and italic. Roman type was modelled from a European scribal manuscript style of the 1400s, based on the pairing of inscriptional capitals used in ancient Rome with Carolingian minuscules developed in the...
) typeface.
Numbers
See Sect. 3.3 of the Standard text.- Numbers should be printed in upright (romanRoman typeIn typography, roman is one of the three main kinds of historical type, alongside blackletter and italic. Roman type was modelled from a European scribal manuscript style of the 1400s, based on the pairing of inscriptional capitals used in ancient Rome with Carolingian minuscules developed in the...
) type.
- ISO 31-0 (after Amendment 2) specifies that "the decimal sign is either the comma on the line or the point on the line". This follows resolution 10 of the 22nd CGPMGeneral Conference on Weights and MeasuresThe General Conference on Weights and Measures is the English name of the Conférence générale des poids et mesures . It is one of the three organizations established to maintain the International System of Units under the terms of the Convention du Mètre of 1875...
, 2003; there is a brief reference to the history of this in http://www.nist.gov/public_affairs/techbeat/tb2006_1122.htm#decimal.
- 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. For this reason, 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.
- For numbers whose magnitude is less than 1, the decimal sign should be preceded by a zero.
- The multiplication sign is either a cross or a half-height dot, though the latter should not be used when the dot is the decimal separator.
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 without a space in between (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
- Products can be written as ab, a b, a⋅b, or a×b. The sign for multiplying numbers is a cross (×) or a half-height dot (⋅). The cross should be used adjacent to numbers if a dot on the line is used as the decimal separator, to avoid confusion between a decimal dot and a multiplication dot.
- Division can be written as
, a/b, or by writing the product of a and b−1, for example a⋅b−1. Numerator or denominator can themselves be products or quotients, but in this case, a solidus (/) should not be followed by a multiplication sign or division sign on the same line, unless parentheses are used to avoid ambiguity.
Mathematical signs and symbols
A comprehensive list of internationally standardized mathematical symbols and notations can be found in ISO 31-11ISO 31-11
ISO 31-11 was the part of international standard ISO 31 that defines mathematical signs and symbols for use in physical sciences and technology...
.