User:Martinvl/Sandbox/Writing quantities in the metric system

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Background
Writers often use shorthand to denote units of measure. Such shorthand can be an abbreviation, such as "in" for "inch" or can be a symbol such as "km" for "kilometre". Symbol are sometimes taken from outside the normal character set in use such as "℥", the symbol for the Apothecaries pound.

The shorthand "in" applies to English only – in Afrikaans for example, the shorthand "dm" is used for the equivalent Afrikaans word "duim". Since both "in" and "dm" are contractions of the same word, but in different languages, they are abbreviations. A symbol on the other hand, defined as "Mark or character taken as the conventional sign of some object or idea or process" applies the appropriate shorthand by substitution rather than by contraction. Since the shorthand for kilometre (Quilômetro in Portuguese or Χιλιόμετρο in Greek) is "km" in both languages and the letter "k" does not appear in the expansion of either translation, "km" is a symbol as it is a substitution rather than a contraction.

Abbreviation development
The use of abbreviations for units of measure emerged once the units themselves were sufficiently widely used that readers understood the abbreviations.

Unless recommendations of a central authority exist and are followed, a single entity can have many different, but equivalent abbeviations. For example, the unit of length, the kilometre first made its appearance in English in 1810 and the compound unit of speed "kilometeres per hour" was in use by 1866. "Kilometres per hour" did not begin to be abbreviated in print until many years later, with several different abbreviations existing near-contemporaneously.

With no central authority to dictate the rules for abbreviations, various publishing houses had their own rules that dictated whether upper case letters, lower case letters, periods and so on shoudl be used, reflecting both changes in fashion and the image of the publishing house concerned.

Development of symbols in metrology
The use of symbols to replace words dates back to at least the late Mediaval era when Johannes Widman, writing in German in 1486, used the symbols "+" and "-" to represent "addition" and "subtraction". In the early 1800s Berzelius introduced a symbolic notation for the chemical elements derived from the elements' Latin names. Typically, "Na" was used for the element sodium (Latin: natrium) and H2O for water.

In 1879, four years after the signing of the Treaty of the Metre, the CIPM proposed a range of symbols for the various metric units then under the auspices of the CGPM. Among these were the use of the symbol "km" for "kilometre", "g" from "gram" and so on.

Prior to 1921, the CGPM were guardians of the international prototype kilogram and metre, the IAU were guardians of time-keeping (which was done using astronomical methods) while the IEC were gaurdians of electrical units of measure. In 1921 the mandate of the CGPM was extended to include all physical units and and over the next few years, the CIPM, on behalf of the CGPM, set about aligning the definitions of the various units of measure and, in conjunction with the IAU, the IEC and other international bodies, made recommendations that ensured a consistent use of units of measure across all physical disciplines. This included the way in which units of measure were written. In 1948, as part of its the preparatory work for the SI, the CGPM adopted symbols for many units of measure that did not have universally-agreed symbols, one of which was the symbol "h" for "hours". At the same time the CGPM formalised the rules for combining units - quotients could be written in one of three formats resulting in "km/h", "km h-1" and "km•h-1" being valid representations of "kilometres per hour". The SI standards, which were MKS-based rather than CGS-based were published in 1960 and have since then have been adopted by many authorities around the globe including academic publishers and legal authorities.

The SI explicitly states that unit symbols are not abbreviations and are to be written using a very specific set of rules. M. Danloux-Dumesnils provides the following justification for this distinction: "It has already been stated that, according to Maxwell, when we write down the result of a measurement, the numerical value multiplies the unit. Hence the name of the unit can be replaced by a kind of algebraic symbol, which is shorter and easier to use in formulae. This symbol is not merely an abbreviation but a symbol which, like chemical symbols, must be used in a precise and prescribed manner."

Measurement shorthand – symbol or abbreviation


In the International System of Units (SI) manual the word "symbol" is used consistently to define the shorthand used to represent the various SI units of measure. The manual also defines the way in which units should be written, the principal rules being:
 * The conventions for upper and lower case letters must be observed – for example 1 MW (megawatts) is equal to 1,000,000,000 mW (milliwatts).
 * No periods should be inserted between letters – for example "m.s" (which is an approximation of "m·s", which correctly uses middle dot) is the symbol for "metres multiplied by seconds", but "ms" is the symbol for milliseconds.
 * No periods should follow the symbol unless the syntax of the sentence demands otherwise (for example a full stop at the end of a sentence).
 * The singular and plural versions of the symbol are identical – not all languages use the letter "s" to denote a plural.

Writing unit symbols and the values of quantities

 * The value of a quantity is written as a number followed by a space (representing a multiplication sign) and a unit symbol; e.g., "2.21 kg", "$7.3 m^{2}$", "22 K". This rule explicitly includes the percent sign (%). Exceptions are the symbols for plane angular degrees, minutes and seconds (°, ′ and ″), which are placed immediately after the number with no intervening space.
 * Symbols for derived units formed by multiplication are joined with a centre dot (·) or a non-break space; e.g., N·m or N m.
 * Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent. E.g., the "metre per second" can be written m/s, m s&minus;1, m·s&minus;1, or $$\textstyle\frac{\mathrm{m}}{\mathrm{s}}$$. Only one solidus should be used; e.g., kg/(m·s2) and kg·m&minus;1·s&minus;2 are acceptable, but kg/m/s2 is ambiguous and unacceptable.
 * Symbols are mathematical entities, not abbreviations, and do not have an appended period/full stop (.).
 * Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic type used for quantities (m for mass, s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.
 * Symbols for units are written in lower case (e.g., "m", "s", "mol"), except for symbols derived from the name of a person. For example, the unit of pressure is named after Blaise Pascal, so its symbol is written "Pa", whereas the unit itself is written "pascal".
 * The one exception is the litre, whose original symbol "l" is unsuitably similar to the numeral "1" or the uppercase letter "i" (depending on the typeface used), at least in many English-speaking countries. The American National Institute of Standards and Technology recommends that "L" be used instead, a usage common in the US, Canada, and Australia (but not elsewhere). This has been accepted as an alternative by the CGPM since 1979. The cursive ℓ is occasionally seen, especially in Japan and Greece, but this is not currently recommended by any standards body. For more information, see litre. The litre is not an SI unit per se and is expressed in SI terms as a cubic decimetre, i.e., dm3.
 * A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator (e.g., "k" in "km", "M" in "MPa", "G" in "GHz"). Compound prefixes are not allowed.
 * All symbols of prefixes larger than 103 (kilo) are uppercase.
 * Symbols of units are not pluralised; e.g., "25 kg", not "25 kgs".
 * The 10th resolution of CGPM in 2003 declared that "the symbol for the decimal marker shall be either the point on the line or the comma on the line." In practice, the decimal point is used in English-speaking countries and most of Asia, and the comma in most of Latin America and in continental European languages.
 * Spaces may be used as a thousands separator (1 000  000) in contrast to commas or periods (1,000,000 or 1.000.000) in order to reduce confusion resulting from the variation between these forms in different countries. In print, the space used for this purpose is typically narrower than that between words (commonly a thin space).
 * Any line-break inside a number, inside a compound unit, or between number and unit should be avoided, but, if necessary, the last-named option should be used.
 * In Chinese, Japanese, and Korean language computing (CJK), some of the commonly used units, prefix-unit combinations, or unit-exponent combinations have been allocated predefined single characters taking up a full square. Unicode includes these in its CJK Compatibility and Letterlike Symbols subranges for back compatibility, without necessarily recommending future usage. These are summarised in Unicode symbols.
 * When writing dimensionless quantities, the terms 'ppb' (parts per billion) and 'ppt' (parts per trillion) are recognised as language-dependent terms, since the value of billion and trillion can vary from language to language. SI, therefore, recommends avoiding these terms. However, no alternative is suggested by the International Bureau of Weights and Measures (BIPM).

Writing the unit names
e.g. "henries" is the plural of "henry". The units lux, hertz, and siemens are exceptions from this rule: they remain the same in singular and plural form. Note that this rule applies only to the full names of units, not to their symbols.
 * Names of units follow the grammatical rules associated with common nouns: in English and in French they start with a lowercase letter (e.g., newton, hertz, pascal), even when the symbol for the unit begins with a capital letter. This also applies to 'degrees Celsius', since 'degree' is the unit. In German however, names of units, in common with all nouns, start with a capital letter.
 * Names of units are pluralised using the normal English grammar rules,
 * When unit names are combined by multiplication, they are separated with a hyphen or a space (e.g. newton-metre or newton metre). The plural is formed by pluralising the last unit name as above (e.g. ten newton-metres).
 * The official US spellings for deca, metre, and litre are deka, meter, and liter, respectively.

Current non-standard representations
Several representations of "kilometres per hour" have been used since the term was introduced and many are still in use today. For example, dictionaries list "km/h", "kmph" and "km/hr" as English abbreviations and the SI representations are 'km/h', '$km h^{-1}$' and '$km•h^{-1}$' and are classified as symbols.

for example style guides of news organisations such as Reuters and The Guardian tend to use "kph" for "kilometres per hour" and "C" or "F" instead of "°C" or "°F" for temperature.