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The metric system is a system of measurement that standardization a set of base units and a nomenclature for describing relatively large and small quantities via decimal-based multiplicative . Though the rules governing the metric system have changed over time, the modern definition, the International System of Units (SI), defines the and seven base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).
An SI derived unit is a named combination of base units such as hertz (cycles per second), newton (kg⋅m/s2), and tesla (1 kg⋅s−2⋅A−1) and in the case of Celsius a shifted scale from Kelvin. Certain units have been officially accepted for use with the SI. Some of these are decimalised, like the litre and electronvolt, and are considered "metric". Others, like the astronomical unit are not. Ancient non-metric but SI-accepted multiples of time, minute and hour, are base 60 (sexagesimal). Similarly, the angular measure degree and submultiples, arcminute, and arcsecond, are also sexagesimal and SI-accepted.
The SI system derives from the older MKS units (MKS) system of units, though the definition of the base units has changed over time. Today, all base units are defined by physical constants; not by prototypes in the form of physical objects as they were in the past.
Other metric system variants include the centimetre–gram–second system of units, the metre–tonne–second system of units, and the gravitational metric system. Each has unaffiliated metric units. Some of these systems are still used in limited contexts.
A notable outlier is the United States (US). Although used in some contexts, the US has resisted full adoption; continuing to use different measurement systems".
Adopting the metric system is known as metrication.
The prefix kilo, for example, implies a factor of 1000 (103), and the prefix milli implies a factor of 1/1000 (10−3). Thus, a kilometre is a thousand metres, and a milligram is one thousandth of a gram. These relations can be written symbolically as:
The historical evolution of metric systems has resulted in the recognition of several principles. A set of independent dimensions of nature is selected, in terms of which all natural quantities can be expressed, called base quantities. For each of these dimensions, a representative quantity is defined as a base unit of measure. The definition of base units has increasingly been realised in terms of fundamental natural phenomena, in preference to copies of physical artefacts. A unit derived from the base units is used for expressing quantities of dimensions that can be derived from the base dimensions of the system—e.g., the square metre is the derived unit for area, which is derived from length. These derived units are coherent, which means that they involve only products of powers of the base units, without any further factors. For any given quantity whose unit has a name and symbol, an extended set of smaller and larger units is defined that are related by factors of powers of ten. The unit of time should be the second; the unit of length should be either the metre or a decimal multiple of it; and the unit of mass should be the gram or a decimal multiple of it.
Metric systems have evolved since the 1790s, as science and technology have evolved, in providing a single universal measuring system. Before and in addition to the SI, other metric systems include: the MKS system of units and the MKSA systems, which are the direct forerunners of the SI; the centimetre–gram–second (CGS) system and its subtypes, the CGS electrostatic (cgs-esu) system, the CGS electromagnetic (cgs-emu) system, and their still-popular blend, the Gaussian units; the metre–tonne–second (MTS) system; and the gravitational metric systems, which can be based on either the metre or the centimetre, and either the gram, gram-force, kilogram or kilogram-force.
It is a coherent system with derived units built from base units using logical rather than empirical relationships and with multiples and submultiples of both units based on decimal factors and identified by a metric prefix.
In 1791 the commission originally defined the metre based on the size of the earth, equal to one ten-millionth of the distance from the equator to the North Pole. In the SI, the standard metre is now defined as exactly of the distance that light travels in a second. The metre can be realised by measuring the length that a light wave travels in a given time, or equivalently by measuring the wavelength of light of a known frequency.
The kilogram was originally defined as the mass of one cubic decimetre of water at 4 °C, standardised as the mass of a man-made artefact of platinum–iridium held in a laboratory in France, which was used until a new definition was introduced in May 2019. Replicas made in 1879 at the time of the artefact's fabrication and distributed to signatories of the Metre Convention serve as de facto standards of mass in those countries. Additional replicas have been fabricated since as additional countries have joined the convention. The replicas were subject to periodic validation by comparison to the original, called the IPK. It became apparent that either the IPK or the replicas or both were deteriorating, and are no longer comparable: they had diverged by 50 μg since fabrication, so figuratively, the accuracy of the kilogram was no better than 5 parts in a hundred million or a relative accuracy of . The revision of the SI replaced the IPK with an exact definition of the Planck constant as expressed in SI units, which defines the kilogram in terms of fundamental constants.
In the early days, multipliers that were positive powers of ten were given Greek-derived prefixes such as kilo- and mega-, and those that were negative powers of ten were given Latin-derived prefixes such as centi- and milli-. However, 1935 extensions to the prefix system did not follow this convention: the prefixes nano- and micro-, for example have Greek roots. (1997). 9780948251849, Picton Publishing. ISBN 9780948251849 During the 19th century the prefix myria-, derived from the Greek word μύριοι ( mýrioi), was used as a multiplier for .
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 below.
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For the most part, the metric prefixes are used uniformly for SI base, derived and accepted units. A notable exception is that for a large measure of seconds, the non-SI units of minute, hour and day are customary instead. Units of duration longer than a day are problematic since both month and year have varying number of days. Sub-second measures are often indicated via submultiple prefixes. For example, millisecond.
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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, which resulted in only one unit of energy being defined – the joule.
Since all gases have the same volume per mole at a given temperature and pressure far from their points of liquefaction and solidification (see Perfect gas), and air is about oxygen (molecular mass 32) and nitrogen (molecular mass 28), the density of any near-perfect gas relative to air can be obtained to a good approximation by dividing its molecular mass by 29 (because ). For example, carbon monoxide (molecular mass 28) has almost the same density as air.
A number of different metric systems have been developed, all using the Mètre des Archives and Kilogramme des Archives (or their descendants) as their base units, but differing in the definitions of the various derived units.
| +Variants of the metric system ! Measure ! SI/MKS ! ! | |||
| distance | metre (m) | centimetre (cm) | metre (m) |
| mass | kilogram (kg) | gram (g) | tonne (t) |
| time | second (s) | second (s) | second (s) |
| velocity | m/s | cm/s | m/s |
| acceleration | m/s2 | gal (Gal) | m/s2 |
| force | newton (N) | dyne (dyn) | sthene (sn) |
| pressure | pascal (Pa) | barye (Ba) | pièze (pz) |
| energy | joule (J) | erg (erg) | kilojoule (kJ) |
| power | watt (W) | erg/s (erg/s) | kilowatt (kW) |
| viscosity | Pa⋅s | poise (P) | pz⋅s |
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 the International System of Electrical and Magnetic Units. During the same period in which the CGS system was being extended to include electromagnetism, other systems were developed, distinguished by their choice of coherent base unit, including the Practical System of Electric Units, or QES (quad–eleventhgram–second) system, was being used. Here, the base units are the quad, equal to (approximately a quadrant of the Earth's circumference), the eleventhgram, equal to , and the second. These were chosen so that the corresponding electrical units of potential difference, current and resistance had a convenient magnitude.
The metre–tonne–second system of units (MTS) was based on the metre, tonne and second – the unit of force was the sthène and the unit of pressure was the pièze. It was invented in France for industrial use and from 1933 to 1955 was used both in France and in the Soviet Union. Gravitational metric systems use the kilogram-force (kilopond) as a base unit of force, with mass measured in a unit known as the hyl, Technische Masseneinheit (TME), mug or metric slug. Although the CGPM passed a resolution in 1901 defining the standard value of Standard gravity to be 980.665 cm/s2, gravitational units are not part of the International System of Units (SI).
The system was promulgated by the General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM) in 1960. At that time, the metre was redefined in terms of the wavelength of a spectral line of the krypton-86 atom (krypton-86 being a stable isotope of an inert gas that occurs in undetectable or trace amounts naturally), and the standard metre artefact from 1889 was retired.
Today, the International system of units consists of 7 base units and innumerable coherent derived units including 22 with special names. The last new derived unit, the katal for catalytic activity, was added in 1999. All the base units except the second are now defined in terms of exact and invariant constants of physics or mathematics, barring those parts of their definitions which are dependent on the second itself. As a consequence, the speed of light has now become an exactly defined constant, and defines the metre as of the distance light travels in a second. The kilogram was defined by a cylinder of platinum-iridium alloy until a new definition in terms of natural physical constants was adopted in 2019. As of 2022, the range of decimal prefixes has been extended to those for 1030 ( quetta–) and 10−30 ( quecto–).
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