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|Metric prefixes in everyday use|
The metric system is an international decimalised system of measurement that was originally based on the mètre des archives and the kilogramme des archives introduced by France in 1799. Over the years, the definitions of the metre and kilogram have been refined and the metric system extended to incorporate many more units. Although a number of variants of the metric system emerged in the late nineteenth and early twentieth centuries the term is now often used as a synonym for the "International System of Units" - the official system of measurement in almost every country in the world.
The United States is the only industrialized country that does not use the metric system as its official system of measurement, although the metric system has been officially sanctioned for use there since 1866. Although the United Kingdom committed to officially adopting the metric system for many measurement applications, it is still not in universal use there and the customary imperial system is still in common and widespread use. Although the originators intended to devise a system that was equally accessible to all, it proved necessary to use prototype units under the custody of government or other approved authorities as standards. Until 1875, control of the prototype units of measure was maintained by the French Government when it passed to an inter-governmental organisation – the Conférence générale des poids et mesures (CGPM). It is now hoped that the last of these prototypes can be retired by 2014.
From its beginning, the main feature of the metric system was the standard set of inter-related base units and a standard set of prefixes in powers of ten. These base units are used to derive larger and smaller units and replaced a huge number of unstandardised units of measure that existed previously. While the system was first developed for commercial use, its coherent set of units made it particularly suitable for scientific and engineering purposes.
The uncoordinated use of the metric system by different scientific and engineering disciplines, particularly in the late 19th century, resulted in different choices of fundamental units, even though all were based on the same definitions of the metre and the kilogram. During the 20th century, efforts were made to rationalise these units and in 1960 the CGPM published the International System of Units ("Système international d'unités" in French, hence "SI") which, since then, has been the internationally recognised standard metric system.
Although the metric system has changed and developed since its inception, its basic concepts have hardly changed - it was designed for transnational use; it consisted of a basic set of units of measurement, now known as base units; derived units were built up from the base units using logical rather than empirical relationships while multiples and submultiples of both base and derived units were decimal based and identified by a standard set of prefixes.
At the outbreak of the French Revolution each country, and in many cases each city, had its own system of measurement. Although different countries might have used the same names for their units of measure such as the foot (or a translation such as pied, fuß, voet, etc.), the sizes of those units varied as did their relationship with their multiples and submultiples, much like the modern-day variation between the US and the UK pint and gallon.
The metric system was, in the words of the French philosopher Condorcet to be "for all people for all time". It was designed for ordinary people, for engineers who worked in human-related measurements and for astronomers and physicists who worked with numbers both small and large, hence the huge range of prefixes that have now been defined in SI.
The metric system was designed to be universal, that is, available to all. When the French Government first investigated the idea of overhauling their system of measurement, Talleyrand, in the late 1780s, acting on Concordet's advice, invited Riggs, a British Parliamentarian and Thomas Jefferson, the American Secretary of State to George Washington, to work with the French in producing an international standard by promoting legislation in their respective legislative bodies. However, these overtures failed and the custody of the metric system remained in the hands of the French Government until 1875.
Unit names are common nouns and use the character set and follow the grammatical rules of the language concerned for example "kilometre", "kilómetro" but to aid universality, each unit has a symbol that is independent of language, for example "km", "V" etc.
The metric system is decimal, except where the non-SI units for time and plane angle measurement are concerned. All multiples and divisions of the decimal units are factors of the power of ten, an idea first proposed by the Flemish mathematician Simon Stevin in 1586.
Decimal prefixes are a characteristic of the metric system; conversions between units of different magnitudes is accomplished by shifting the decimal point or changing an exponent; for example, the speed of light may be expressed as 299792.458 km/s or 2.99792458×108 m/s. This is done at the cost of losing the simplicity associated with many traditional systems of units where division by 3 or 4 does not result in awkward fractions; for example one third of a foot is four inches.
In 1854, the mathemetican de Morgan, when summarised the advantages of a decimal-based system over a non-decimal system "In the simple rules of arithmetic, we practice a pure decimal system, nowhere interrupted by the entrance of any other system: from column to column we never carry anything but tens".
|Metric prefixes in everyday use|
A common set of decimal-based prefixes is applied to some units which are too large or too small for practical use without adjustment. The effect of the prefixes is to multiply or divide the unit by a factor of ten, one hundred or an integer power of one thousand. (This idea was first suggested by Mouton in 1670.) The prefix kilo, for example, is used to multiply the unit by 1000, and the prefix milli is to indicate a one-thousandth part of the unit. Thus the kilogram and kilometre are a thousand grams and metres respectively, and a milligram and millimetre are one thousandth of a gram and metre respectively. These relations can be written symbolically as:
When applying prefixes to derived units of area and volume that are expressed in terms of units of length squared or cubed, the square and cube operators are applied to the unit of length including the prefix, as illustrated here:
Prefixes are not usually used to indicate multiples of a second greater than 1; the non-SI units of minute, hour and day are used instead. On the other hand, prefixes are used for multiples of the non-SI unit of volume, the litre (l, L), or the stere (cubic metre). Examples:
Initially positive powers of ten had Greek-derived prefixes and negative power of ten Latin-derived prefixes. The most familiar prefixes in everyday use are kilo- and mega-, which are of Greek origin, and centi- and milli-, which are of Latin origin. However, later SI extensions to the prefix system did not follow the Latin-less-than-one convention; instead, such prefixes (nano- and micro-, for example) use prefixes with Greek roots.
The initial way to establish a standard was to make prototypes of the base units and distribute copies to approved centres. This made the new standard reliant on the original prototypes, which would be in conflict with the previous goal, since all countries would have to refer to the one holding the prototypes.
Instead, where possible, definitions of the base units were developed so that any laboratory equipped with proper instruments would be able to construct their own copies of the standard. In the original version of the metric system the base units could be derived from a specified length (the metre) and the weight [mass] of a specified volume (1⁄1000 of a cubic metre) of pure water. Initially the Assemblée Constituante considered defining the metre as the length of a pendulum that has a period of one second at 45°N and an altitude equal to sea level. The altitude and latitude were specified to accommodate variations in gravity – the specified latitude was a compromise between the latitude of London (51° 30'N), Paris (48° 50'N) and the median parallel of the United States (38°N) to accommodate variations. However Borda persuaded the Assemblée Constituante that a survey having its ends at sea level and based on a meridian that spanned at least 10% of the earth's quadrant would be more appropriate for such a basis.
The base units used in the metric system must be realisable, ideally with reference to natural phenomena rather than unique artifacts. Each of the base units in SI is accompanied by a mise en pratique published by the BIPM that describes in detail at least one way in which the base unit can be measured.
Two of the base units originally depended on artifacts – the metre and the kilogram. The original prototypes of each artifact were adopted in 1799 and replaced in 1889. The 1889 prototypes used the best technology of the day to ensure stability.
In 1889 there was no generally accepted theory regarding the nature of light but by 1960 the wavelength of specific light spectra could give a more accurate and reproducible value than a prototype metre. In that year the prototype metre was replaced by a formal definition which defines the metre in terms of the wavelength of specified light spectra. By 1983 it was accepted that the speed of light was constant and that this provided a more reproducible procedure for measuring length, the metre was redefined in terms of the speed of light. These definitions give a much better reproducibility and also allow anyone, anywhere to make their own "standard" metre (assuming that they have a good enough laboratory).
Similarly, at the 13th convocation of the CGPM in 1968, the definitive second was redefined in terms of measurements taken from atomic clocks rather than from the earth's rotation; in 2008 the solar day was 0.002 s longer than in 1820 but it was only in the 1960s that this could be measured more accurately using clocks rather than relying on astronomy.
Each variant of the metric system has a degree of coherence – the various derived units being directly related to the base units without the need of intermediate conversion factors. For example, in a coherent system the units of force, energy and power are chosen so that the equations
hold without the introduction of constant factors. Once a set of coherent units have been defined, other relationships in physics that use those units will automatically be true - Einstein's mass-energy equation, E = mc2, does not require extraneous constants when expressed in coherent units.
The cgs system had two units of energy, the erg that was related to mechanics and the calorie that was related to thermal energy so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI resulting in only one unit of energy being defined - the joule.
In SI, which is a coherent system, the unit of power is the "watt" which is defined as "one joule per second". In the foot-pound-second system of measurement, which is non-coherent, the unit of power is the "horsepower" which is defined as "550 foot-pounds per second", the pound in this context being the pound-force.
The concept of coherence was only introduced into the metric system in the third quarter of the nineteenth century; in its original form the metric system was non-coherent - in particular the litre was 0.001 m3 and the are (from which we get the hectare) was 100 m2. A precursor to the concept of coherence was however present in that the units of mass and length were related to each other through the physical properties of water, the gram having been designed as being the mass of one cubic centimetre of water at its freezing point.
The metric system is very similar to the units of measurement used in Mesopotamia about five millennia previously: for example, a metre is almost exactly 1 Mesopotamian step, a litre is almost exactly 1 Mesopotamian bowl, and a metric pound is almost exactly 1 Mesopotamian pound or 1/2 kilograms.
In 1586, the Flemish mathematician Simon Stevin published a small pamphlet called De Thiende ("the tenth"). Decimal fractions had been employed for the extraction of square roots some five centuries before his time, but nobody used decimal numbers in daily life. Stevin declared that using decimals was so important that the universal introduction of decimal weights, measures and coinage was only a matter of time.
The idea of a metric system was proposed by John Wilkins, first secretary of the Royal Society of London in 1668. Two years later, in 1670, Gabriel Mouton, a French abbot and scientist, proposed a decimal system of measurement based on the circumference of the Earth. His suggestion was that a unit, the milliare, be defined as a minute of arc along a meridian. He then suggested a system of sub-units, dividing successively by factors of ten into the centuria, decuria, virga, virgula, decima, centesima, and millesima. His ideas attracted interest at the time, and were supported by both Jean Picard and Christiaan Huygens in 1673, and also studied at the Royal Society in London. In the same year, Gottfried Leibniz independently made proposals similar to those of Mouton.
In pre-revolutionary Europe, each state had its own system of units of measure. Some countries, such as Spain and Russia, saw the advantages of harmonising their units of measure with those of their trading partners. However, vested interests who profited from variations in units of measure opposed this. This was particularly prevalent in France where there was a huge inconsistency in the size of units of measure. During the early years of the French Revolution, the leaders of the French revolutionary Assemblée Constituante decided that rather than standardising the size of the existing units, they would introduce a completely new system based on the principles of logic and natural phenomena.
Initially France attempted to work with other countries towards the adoption of a common set of units of measure. Among the supporters of such an international system of units was Thomas Jefferson who, in 1790, presented a document Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States to congress in which he advocated a decimal system that used traditional names for units (such as ten inches per foot). The report was considered but not adopted by Congress. There was little support from other countries.
The law of 18 Germinal, Year III (7 April 1795) defined five units of measure:
This system continued the tradition of having separate base units for geometrically related dimensions, e.g., metre for lengths, are (100 m2) for areas, stère (1 m3) for dry capacities, and litre (1 dm3) for liquid capacities. The hectare, equal to a hundred ares, is the area of a square 100 metres on a side (about 2.47 acres), and is still in use. The early metric system included only a few prefixes from milli (one thousandth) to myria (ten thousand), and they were based on powers of 10 unlike later prefixes added in the SI, which are based on powers of 1,000.
Originally the kilogram was called the "grave"; the "gram" being an alternative name for a thousandth of a grave. However, the word "grave", being a synonym for the title "count" had aristocratic connotations and was renamed the kilogram.
France officially adopted the metric system on 10 December 1799 with conversion being mandatory first in Paris and then across the provinces.
The areas that were annexed by France during the Napoleonic era inherited the metric system. In 1812, Napoleon introduced a system known as mesures usuelles which used the names of pre-metric units of measure, but defined them in terms of metric units – for example, the livre metrique (metric pound) was 500 g and the toise metrique (metric fathom) was 2 metres. After the Congress of Vienna in 1815, France lost the territories that she had annexed; some, such as the Papal States reverted to their pre-revolutionary units of measure, others such as Baden adopted a modified version of the mesures usuelles, but France kept her system of measurement intact.
In 1817, the Netherlands reintroduced the metric system, but used pre-revolutionary names – for example 1 cm became the duim (thumb), the ons (ounce) became 100 g and so on. Certain German states adopted similar systems and in 1852 the German Zollverein (customs union) adopted the zollpfund (customs pound) of 500 g for intrastate commerce. In 1872 the newly formed German Empire adopted the metric system as its official system of weights and measures and the newly formed Kingdom of Italy likewise, following the lead given by Piedmont, adopted the metric system in 1861.
The Exposition Universelle (1867) (Paris exhibition) devoted a stand to the metric system and by 1875 two thirds of the European population and close on half the world's population had adopted the metric system. By 1872 the principal European countries not to have adopted the metric system were Russia and the United Kingdom.
The first attempt to have the US adopt the metric system was in the late 1920s by The General Federation of Women's Clubs for the US to adopt the metric system sending 100,000 petitions to Congress in 1927 with over seven million signatures. This first effort as with all future efforts failed as the old system had too much tradition behind it.
In 1861, a committee of the British Association for Advancement of Science (BAAS) including William Thomson (later Lord Kelvin), James Clerk Maxwell and James Prescott Joule introduced the concept of a coherent system of units based on the metre, gram and second which, in 1873, was extended to include electrical units.
On 20 May 1875 an international treaty known as the Convention du Mètre (Metre Convention) was signed by 17 states. This treaty established the following organisations to conduct international activities relating to a uniform system for measurements:
In 1881, first International Electrical Congress adopted the BAAS recommendations on electrical units, followed by a series of congresses in which further units of measure were defined.
A number of variants of the metric system evolved, all using the Mètre des Archives and Kilogramme des Archives as their base units, but differing in the definitions of the various derived units.
|Variants of the metric system|
The centimetre gram second system of units (CGS) was the first coherent metric system, having been developed in the 1860s and promoted by Maxwell and Thomson. In 1874 this system was formally promoted by the British Association for the Advancement of Science (BAAS). The system's characteristics are that density is expressed in g/cm3, force expressed in dynes and mechanical energy in ergs. Thermal energy was defined in calories, one calorie being the energy required to raise the temperature of one gram of water from 15.5 °C to 16.5 °C. The meeting also proposed two sets of units for electrical and magnetic properties - the electrostatic set of units and the electromagnetic set of units.
The cgs units of electricity were cumbersome to work with. This was remedied at the 1893 International Electrical Congress held in Chicago by defining the "international" ampere and ohm using definitions based on the metre, kilogram and second. In 1901, Giorgi showed that by adding an electrical unit as a fourth base unit, the various anomalies in electromagnetic systems could be resolved. The metre-kilogram-second-coulomb (MKSC) and metre-kilogram-second-ampere (MKSA) systems are examples of such systems.
The International System of Units (System international units or SI) is the current international standard metric system and the system most widely used around the world. It is an extension of Giorgi's MKSA system; its base units are the metre, kilogram, second, ampere, kelvin, candela and mole. Proposals have been made to change the definitions of four of the base units at the 24th meeting of the CGPM in October 2011. These changes should not affect the average person.
The metre-tonne-second system of units (MTS) was based on the metre, tonne and second - the unit of force is the sthène and the unit of pressure is the pièze. It was invented in France in industry and was mostly used in the Soviet Union from 1933 to 1955.
Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl, TME, mug or metric slug. Note these are not part of the International System of Units (SI).
The 9th CGPM met in 1948, fifteen years after the 8th CGPM. In response to formal requests made by the International Union of Pure and Applied Physics and by the French Government to establish a practical system of units of measure, the CGPM requested the CIPM to prepare recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention. At the same time the CGPM formally adopted a recommendation for the writing and printing of unit symbols and of numbers. The recommendation also catalogued the recommended symbols for the most important MKS and CGS units of measure and for the first time the CGPM made recommendations concerning derived units.
The CIPM's draft proposal, which was an extensive revision and simplification of the metric unit definitions, symbols and terminology based on the MKS system of units, was put to the 10th CGPM in 1954. In accordance with Giorgi's proposals of 1901, the CIPM also recommended that the ampere be the base unit from which electromechanical would be derived. The definitions for the ohm and volt that had previously been in use were discarded and these units became derived units based on the metre, ampere, second and kilogram. After negotiations with the CIS and IUPAP, two further base units, the degree kelvin and the candela were also proposed as base units. The full system and name "Système International d'Unités" were adopted at the 11th CGPM. During the years that followed the definitions of the base units and particularly the mise en pratique to realise these definitions have been refined.
The formal definition of International System of Units (SI) along with the associated resolutions passed by the CGPM and the CIPM are published by the BIPM on the Internet and in brochure form at regular intervals. The eighth edition of the brochure Le Système International d'Unités - The International System of Units was published in 2006.
Although SI, as published by the CGPM, should, in theory, meet all the requirements of commerce, science and technology, certain units of measure have acquired such a position within the world community that it is likely they will be used for many years to come. In order that such units be used consistently around the world, the SI Brochure, the CGPM catalogued such units in the SI brochure. The 8th edition of the brochure catalogued the following categories:
When the metre was redefined in 1960, the kilogram was the only SI base unit that relied on a specific artifact. Moreover, after the 1996-1998 recalibration a clear divergence between the various prototype kilograms was observed.
At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artifacts that were then in use. At a meeting of the CCU held in Reading, United Kingdom in September 2010, a resolution and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle. The proposals that the CCU put forward were:
The CIPM meeting of October 2010 found that "the conditions set by the General Conference at its 23rd meeting have not yet been fully met. For this reason the CIPM does not propose a revision of the SI at the present time". The CIPM did however sponsor a resolution at the 24th CGPM in which the changes were agreed in principle and which were expected to be finalised at the CGPM's next meeting in 2014.
The usage of the metric system varies around the world. According to the US Central Intelligence Agency's Factbook, the International System of Units has been adopted as the official system of weights and measures by all nations in the world except for Burma, Liberia and the United States, while NIST has claimed that the United States is the only industrialized country where the metric system is not the official system of units. Some sources, though, suggest that this information is out of date. An Agence France-Presse report from 2010 stated that Sierra Leone, not Liberia, had continued to use the Imperial system, but had passed a law to enact metrication, in line with its Mano River Union (MRU) neighbours Guinea and Liberia. Reports from Burma suggest that that country is planning to adopt the metric system also.
In the United States, where the use of metric units was authorised by Congress in 1866, such units are widely used in science, military, and partially in industry, but customary units predominate in household use. At retail stores, the liter is a commonly used unit for volume, especially on bottles of beverages, and milligrams are used to denominate the amounts of medications, rather than grains. Also, other standardised measuring systems other than metric are still in universal international use, such as nautical miles and knots in international aviation.
In the countries of the Commonwealth of Nations the metric system has replaced the imperial system by varying degrees: Australia, New Zealand and Commonwealth countries in Africa are almost totally metric, India is mostly metric, Canada is partly metric while in the United Kingdom the metric system, the use of which was first permitted for trade in 1864, is used in much government business, in most industries including building, health and engineering and for pricing by measure or weight in most trading situations, both wholesale and retail. However the imperial system is often used by journalists and continues to be used in many unregulated applications.
A number of other jurisdictions, such as Hong Kong, have laws mandating or permitting other systems of measurement in parallel with the metric system in some or all contexts.
The SI symbols for the metric units are intended to be identical, regardless of the language used but unit names are common nouns and use the character set and follow the grammatical rules of the language concerned. For example, the SI unit symbol for kilometre is "km" everywhere in the world, even though the local language word for the unit name may vary. Language variants for the kilometre unit name include: chilometro (Italian), Kilometer (German)[Note 1], kilometer (Dutch), kilomètre (French), χιλιόμετρο (Greek), quilómetro/quilômetro (Portuguese) and Километр (Russian).
Variations are also found with the spelling of unit names in countries using the same language, including differences in American English and British spelling. For example meter and liter are used in the United States whereas metre and litre are used in other English-speaking countries. In addition, the official US spelling for the rarely used SI prefix for ten is deka. In American English the term metric ton is the normal usage whereas in other varieties of English tonne is common. Gram is also sometimes spelled gramme in English-speaking countries other than the United States, though this older usage is declining.
The dual usage of metric and non metric units has resulted in serious errors. These include:
During its evolution, the metric system has adopted many units of measure. The introduction of SI rationalised both the way in which units of measure were defined and also the list of units in use. These are now catalogued in the official SI Brochure. The table below lists the units of measure in this catalogue and shows the conversion factors connecting them with the equivalent units that were in use on the eve of the adoption of SI.
|Quantity||Dimension||SI unit and symbol||Legacy unit and symbol||Conversion|
|Time||second (s)||second (s)||1|
|Length||metre (m)||centimetre (cm)|
|Mass||kilogram (kg)||gram (g)||0.001|
|Electric current||ampere (A)||international ampere|
abampere or biot
degrees Celsius (°C)
|centigrade (°C)||[K] = [°C] + 273.15|
|Luminous intensity||candela (cd)||international candle||0.982|
|Amount of substance||mole (mol)||No legacy unit||n/a|
|Area||square metre (m2)||are (are)||100|
|Frequency||hertz (Hz)||cycles per second||1|
|Energy||joule (J)||erg (erg)||10−7|
|Force||newton (N)||dyne (dyn)|
|Pressure||pascal (Pa)||barye (Ba)|
|Electric charge||coulomb (C)||abcoulomb|
statcoulomb or franklin
|Potential difference||volt (V)||international volt|
|Electric resistance||ohm (Ω)||international ohm|
|Electric conductance||siemens (S)||international mho (℧)|
|Magnetic flux||weber (Wb)||maxwell (Mx)||10−8|
|Magnetic flux density||tesla (T)||gauss (G)||1×10−4|
|Magnetic field strength||(A/m)||oersted (Oe)||103/4π = 79.57747|
|Dynamic viscosity||(Pa·s)||poise (P)||0.1|
|Kinematic viscosity||(m2s−1)||stokes (St)||10−4|
|Luminous flux||lumen (lm)||stilb (sb)||104|
|Illuminance||lux (lx)||phot (ph)||104|
|[Radioactive] activity||becquerel (Bq)||curie (Ci)||3.70×1010|
|Absorbed [radiation] dose||gray (Gy)||roentgen (R)|
|Radiation dose equivalent||sievert||roentgen equivalent man (rem)||0.01|
|Catalytic activity||katal (kat)||No legacy unit||n/a|
The SI Brochure also catalogues certain non-SI units that are widely used with the SI in matters of everyday life or units that are exactly defined values in terms of SI units and are used in particular circumstances to satisfy the needs of commercial, legal, or specialised scientific interests. These units include:
|Quantity||Dimension||Unit and symbol||Equivalence|
|Mass||tonne (t)||1000 kg|
|Area||hectare (ha)||0.01 km2|
|Volume||litre (L or l)||0.001 m3|
|Plane angle||degree (°)|