The metric system is an internationally adopted decimal system of
measurement. It is in widespread use, and where it is used, it is the
only or most common system of weights and measures. It is now known as
the
Contents 1 Units 1.1 Base units
1.2
2 Realisation of units 3 Properties as a system 3.1 Units based on the natural world
3.2 Base and derived unit structure
3.3
4 International
4.1 Historical variants 4.1.1 Gaussian second and the first mechanical system of units 4.1.2 The EMU, ESU and Gaussian systems of electrical units 4.1.3 Centimetre–gram–second systems 4.1.4 International system of electrical units 4.1.5 MKS and MKSA systems 4.1.6 Metre–tonne–second systems 4.1.7 Gravitational systems 5 Relating SI to the real world 6 Conversion table 7 See also 8 Notes 9 References 10 External links Units[edit]
Base units[edit]
The modern metric system consists of four electromechanical base units
representing four fundamental dimensions of measure: length, mass,
time and electromagnetism. The units are the metre for length,
kilogram for mass, second for time, and ampere for electromagnetism.
Together they are capable of measuring any known quantity. There are
also three additional supplemental base units which are not
independent: the kelvin, a thermodynamic measure; the candela, a
measure of irradiance; and the mole, representing a quantity of
substance.
volt, a unit of electrical potential ohm, a unit of electrical resistance tesla, a unit of magnetic flux density weber, a unit of magnetic flux farad, a unit of electrical capacitance henry, a unit of electrical inductance siemens, a unit of electrical conductance (the inverse of ohm) coulomb, a unit of electrical charge Four of these units are mechanical quantities: watt, a unit of mechanical or electrical power newton, a unit of mechanical force joule, a unit of mechanical, electrical or thermodynamic energy pascal, a unit of pressure Five units represent measures of electromagnetic radiation: becquerel, a unit of radioactive decay sievert, a unit of absorbed ionising radiation gray, a unit of ionising radiation lux, a unit of luminous flux lumen, a unit of luminous intensity Two units are measures of circular arcs and spherical surfaces: radian, a unit of circular arc steradian, a unit of spherical surface area Three units are miscellaneous: degree Celsius, a unit of thermodynamic temperature katal, a unit of catalytic activity (enzymatic) hertz, a unit of cycles per second (inverse of second) Auxiliary and accessory units[edit] Main article: Non-SI units mentioned in the SI Although SI, as published by the CGPM, should, in theory, meet all the requirements of commerce, science and technology, certain customary units of measure have acquired established positions within the world community. In order that such units are used consistently around the world, the CGPM catalogued such units in Tables 6 to 9 of the SI brochure. These categories are:[1] Non-SI units accepted for use with the International
The SI symbols for the metric units are intended to be identical,
regardless of the language used[2] but unit names are ordinary 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), kilómetro (Spanish) and
километр (Russian).[3][4]
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.
The metre was originally defined to be one ten millionth of the
distance between the
Main article: Realisation (metrology)
The base units used in the metric system must be realisable. Each of
the definitions of the base units in SI is accompanied by a defined
mise en pratique [practical realisation] that describes in detail at
least one way in which the base unit can be measured.[12] Where
possible, definitions of the base units were developed so that any
laboratory equipped with proper instruments would be able to realise a
standard without reliance on an artefact held by another country. In
practice, such realisation is done under the auspices of a mutual
acceptance arrangement (MAA).[13]
The standard metre is defined as exactly 1/299,792,458 of the distance
that light travels in a second. The realisation of the metre depends
in turn on precise realisation of the second. There are both
astronomical observation methods and laboratory measurement methods
that are used to realise units of the standard metre. Because the
speed of light is now exactly defined in terms of the metre, more
precise measurement of the speed of light does not result in a more
accurate figure for its velocity in standard units, but rather a more
accurate definition of the metre. The accuracy of the measured speed
of light is considered to be within 1 m/s, and the realisation of
the metre is within about 3 parts in 1,000,000,000, or an order of
10−9 parts.
The kilogram is defined by the mass of a man-made artefact of
platinum-iridium held in a laboratory in France. Replicas made in 1879
at the time of the artefact's fabrication and distributed to
signatories of the
Metric prefixes in everyday use Text Symbol Factor Power exa E 7018100000000000000♠1000000000000000000 1018 peta P 7015100000000000000♠1000000000000000 1015 tera T 7012100000000000000♠1000000000000 1012 giga G 7009100000000000000♠1000000000 109 mega M 7006100000000000000♠1000000 106 kilo k 7003100000000000000♠1000 103 hecto h 100 102 deca da 10 101 (none) (none) 1 100 deci d 0.1 10−1 centi c 0.01 10−2 milli m 0.001 10−3 micro μ 6994100000000000000♠0.000001 10−6 nano n 6991100000000000000♠0.000000001 10−9 pico p 6988100000000000000♠0.000000000001 10−12 femto f 6985100000000000000♠0.000000000000001 10−15 atto a 6982100000000000000♠0.000000000000000001 10−18 v t e A common set of decimal-based prefixes that have the effect of
multiplication or division by an integer power of ten can be applied
to units that are themselves too large or too small for practical use.
The concept of using consistent classical (
1 mg = 0.001 g 1 km = 1000 m 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.[15] During the 19th century the prefix myria-, derived from the Greek word μύριοι (mýrioi), was used as a multiplier for 7004100000000000000♠10000.[16] 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.[14] 1 mm2 (square millimetre) = (1 mm)2 = (0.001 m)2 = 6994100000000000000♠0.000001 m2 1 km2 (square kilometre) = (1 km)2 = (1000 m)2 = 7006100000000000000♠1000000 m2 1 mm3 (cubic millimetre) = (1 mm)3 = (0.001 m)3 = 6991100000000000000♠0.000000001 m3 1 km3 (cubic kilometre) = (1 km)3 = (1000 m)3 = 7009100000000000000♠1000000000 m3 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) such as millilitres (ml).[14] Coherence[edit] Main article: Coherence (units of measurement)
Each variant of the metric system has a degree of coherence—the various derived units are directly related to the base units without the need for intermediate conversion factors.[17] For example, in a coherent system the units of force, energy and power are chosen so that the equations force = mass × acceleration energy = force × distance power = energy ÷ time hold without the introduction of unit conversion factors. Once a set
of coherent units have been defined, other relationships in physics
that use those units will automatically be true. Therefore, Einstein's
mass-energy equation, E = mc2, does not require extraneous
constants when expressed in coherent units.[18]
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.[6]
Rationalisation[edit]
Maxwell's equations of electromagnetism contained a factor relating to
steradians, representative of the fact that electric charges and
magnetic fields may be considered to emanate from a point and
propagate equally in all directions, i.e. spherically. This factor
appeared awkwardly in many equations of physics dealing with the
dimensionality of electromagnetism and sometimes other things.
"Completeness"[edit]
The four dimensions of length, time, mass and electromagnetism
underlie everything realisable, and together form the system of
electromechanical units. These dimensions have an irreducible
relationship to the physical world; there must be one unit for each,
or some things will not be sensibly measurable, and the system will
fall into chaos or contradiction. Nothing that we know of requires
another (fifth) orthogonal dimension and unit of measure. But because
some kinds of perceptual phenomena do not have readily quantifiable
dimensions in the electromechanical units, additional human-perceptual
base units were defined: one for temperature, illumination, and
quantity of substance.
International
Variants of the metric system Quantity CGS MKS MTS distance, displacement, length, height, etc. (d, x, l, h, etc.) centimetre (cm) metre (m) metre mass (m) gram (g) kilogram (kg) tonne (t) time (t) second (s) second second speed, velocity (v, v) cm/s m/s m/s acceleration (a) gal (Gal) m/s2 m/s2 force (F) dyne (dyn) newton (N) sthene (sn) pressure (P or p) barye (Ba) pascal (Pa) pièze (pz) energy (E, Q, W) erg (erg) joule (J) kilojoule (kJ) power (P) erg/s watt (W) kilowatt (kW) viscosity (μ) poise (P) Pa⋅s pz⋅s Gaussian second and the first mechanical system of units[edit]
In 1832, Gauss used the astronomical second as a base unit in defining
the gravitation of the earth, and together with the gram and
millimetre, became the first system of mechanical units.
The EMU, ESU and Gaussian systems of electrical units[edit]
Several systems of electrical units were defined following discovery
of Ohm's law in 1824.
Centimetre–gram–second systems[edit]
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).[19] The system's characteristics are that density is expressed
in g/cm3, force expressed in dynes and mechanical energy in ergs.
Flying an overloaded American International Airways aircraft from
Miami,
Conversion table[edit] Main article: Conversion of units 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.[6] 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.[32][33][34][35] Quantity Dimension SI unit and symbol Legacy unit and symbol Conversion factor Time T second (s) second (s) 1 Length L metre (m) centimetre (cm) ångström (Å) 0.01 10−10 Mass M kilogram (kg) gram (g) 0.001 Electric current I ampere (A) international ampere abampere or biot statampere 7000100002200000000♠1.000022 10.0 6990333564100000000♠3.335641×10−10 Temperature
Θ
kelvin (K)
degree
Luminous intensity J candela (cd) international candle 0.982 Amount of substance N mole (mol) No legacy unit n/a Area L2 square metre (m2) are (a)[36] 100 Acceleration LT−2 (m⋅s−2) gal (gal) 10−2 Frequency T−1 hertz (Hz) cycles per second 1 Energy L2MT−2 joule (J) erg (erg) 10−7 Power L2MT−3 watt (W) (erg/s) horsepower (HP) Pferdestärke (PS) 10−7 745.7 735.5 Force LMT−2 newton (N) dyne (dyn) sthene (sn) kilopond (kp) 10−5 103 7000980665000000000♠9.80665 Pressure L−1MT−2 pascal (Pa) barye (Ba) pieze (pz) atmosphere (at) 0.1 103 7005101325000000000♠1.01325×105 Electric charge IT coulomb (C) abcoulomb statcoulomb or franklin 10 6990333564100000000♠3.335641×10−10 Potential difference L2MT−3I−1 volt (V) international volt abvolt statvolt 7000100034000000000♠1.00034 10−8 7002299792500000000♠2.997925×102 Capacitance L−2M−1T4I2 farad (F) abfarad statfarad 109 6988111265000000000♠1.112650×10−12 Inductance L2MT−2I−2 henry (H) abhenry stathenry 10−9 7011898755200000000♠8.987552×1011 Electric resistance L2MT−3I−2 ohm (Ω) international ohm abohm statohm 7000100049000000000♠1.00049 10−9 7011898755200000000♠8.987552×1011 Electric conductance L−2M−1T3I2 siemens (S) international mho (℧) abmho statmho 6999999510000000000♠0.99951 109 6988111265000000000♠1.112650×10−12 Magnetic flux L2MT−2I−1 weber (Wb) maxwell (Mx) 10−8
Dynamic viscosity ML−1T−1 (Pa⋅s) poise (P) 0.1 Kinematic viscosity L2T−1 (m2⋅s−1) stokes (St) 10−4 Luminous flux J lumen (lm) stilb (sb) 104 Illuminance JL−2 lux (lx) phot (ph) 104 [Radioactive] activity T−1 becquerel (Bq) curie (Ci) 7010370000000000000♠3.70×1010 Absorbed [radiation] dose L2T−2 gray (Gy) roentgen (R) rad (rad) ≈0.01[Note 4] 0.01 Radiation dose equivalent L2T−2 sievert roentgen equivalent man (rem) 0.01 Catalytic activity NT−1 katal (kat) enzyme unit(U) 1/60μkat 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:[6] Quantity Dimension Unit and symbol Equivalence Mass M tonne (t) 7003100000000000000♠1000 kg Area L2 hectare (ha) 0.01 km2 104 m2 Volume L3 litre (L or l) 0.001 m3 Time T minute (min) hour (h) day (d) 60 s 7003360000000000000♠3600 s 7004864000000000000♠86400 s Pressure L−1MT−2 bar 100 kPa Plane angle none degree (°) minute (′) second (″) (π⁄180) rad (π⁄7004108000000000000♠10800) rad (π⁄7005648000000000000♠648000) rad See also[edit] Binary prefix, used in computer science History of measurement ISO/IEC 80000, style manual for measurements metric and non-metric, superseding ISO 31 Metrology Units of measurement Notes[edit] ^ In German all nouns start with an upper-case letter ^ Non-SI units for time and plane angle measurement, inherited from existing systems, are an exception to the decimal-multiplier rule ^ A stable isotope of an inert gas that occurs in undetectable or trace amounts naturally ^ Roentgen is a measure of ionisation (charge per mass), not of absorbed dose, so there is no well-defined conversion factor. However, a radiation field of gamma rays that produces 1 roentgen of ionisation in dry air would deposit 0.0096 gray in soft tissue, and between 0.01 and 0.04 grays in bone. Since this unit was often used in radiation detectors, a factor of 0.01 can be used to convert the detector reading in roentgens to the approximate absorbed dose in grays. References[edit] ^
External links[edit] Wikiversity has learning resources about Using the Metric System CBC Radio Archives For Good Measure: Canada Converts to Metric
US Metric Association
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