Metric system
The metric system is a
Prefixes for multiples and submultiples
In the metric system, multiples and submultiples of units follow a decimal pattern.[a]
Prefix | Symbol | Factor | Power |
---|---|---|---|
tera | T | 1000000000000 | 1012 |
giga | G | 1000000000 | 109 |
mega | M | 1000000 | 106 |
kilo | k | 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 | 0.000001 | 10−6 |
nano | n | 0.000000001 | 10−9 |
pico | p | 0.000000000001 | 10−12 |
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 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
Definitions of the metric system units
The decimalised system based on the metre, which had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the International System of Units (SI) in the mid-20th century, under the oversight of an international standards body. Adopting the metric system is known as metrication.
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
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, metric systems include: the
The SI has been adopted as the official system of weights and measures by nearly all nations in the world.
History of the current metric system
The
The units of the metric system, originally taken from observable features of nature, are now defined by seven
The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units. It is a
The metric system is extensible, and new derived units are defined as needed in fields such as radiology and chemistry. For example, the katal, a derived unit for catalytic activity equivalent to one mole per second (1 mol/s), was added in 1999.[5]
Principles
Although the metric system has changed and developed since its inception, its basic concepts have hardly changed. Designed for transnational use, it consisted of a basic set of
Realisation
The base units used in a measurement system must be realisable. Each of the definitions of the base units in the 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.[8] 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.[9] In the SI, the standard metre is defined as exactly 1⁄299792458 of the distance that light travels in a second.[10][11] 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.[12]
The
Base and derived unit structure
A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others. A base unit is a unit adopted for expressing a base quantity. A derived unit is used for expressing any other quantity, and is a product of powers of base units. For example, in the modern metric system, length has the unit metre and time has the unit second, and speed has the derived unit metre per second.[6]: 15 Density, or mass per unit volume, has the unit kilogram per cubic metre.[6]: 434
Decimal ratios
A characteristic feature of metric systems is their reliance upon multiples of 10. For example, the base unit of length is the metre, and distances much longer or much shorter than 1 metre are measured in units that are powers of 10 times a metre. This is unlike older systems of units in which the ratio between the units for longer and shorter distances varied: there are 12 inches in a foot, but the number of 5,280 feet in a mile is not a power of 12.[6]: 17 For many everyday applications, the United States has resisted the adoption of a decimal-based system, continuing to use "a conglomeration of basically incoherent measurement systems".[16]
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.
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.[2]
1 mm2 (square millimetre) | = (1 mm)2 | = (0.001 m)2 | = 0.000001 m2 |
1 km2 (square kilometre) | = (1 km)2 | = (1000 m)2 | = 1000000 m2 |
1 mm3 (cubic millimetre) | = (1 mm)3 | = (0.001 m)3 | = 0.000000001 m3 |
1 km3 (cubic kilometre) | = (1 km)3 | = (1000 m)3 | = 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).[2]
Coherence
Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors.[18] 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 |
energy | = | power | × | time |
hold without the introduction of unit conversion factors. Once a set of coherent units has been defined, other relationships in physics that use this set of units will automatically be true. Therefore, Einstein's mass–energy equation, E = mc2, does not require extraneous constants when expressed in coherent units.[19]
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.[20]
Rationalisation
Maxwell's equations of electromagnetism contained a factor of 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 made equations more awkward than necessary, and so Oliver Heaviside suggested adjusting the system of units to remove it.[21]
Common notions
The basic units of the metric system, as originally defined, represented common quantities or relationships in nature. They still do – the modern precisely defined quantities are refinements of definition and methodology, but still with the same magnitudes. In cases where laboratory precision may not be required or available, or where approximations are good enough, the original definitions may suffice.[b]
- A second is 1/60 of a minute, which is 1/60 of an hour, which is 1/24 of a day, so a second is 1/86400 of a day (the use of base 60 dates back to Babylonian times); a second is the time it takes a dense object to freely fall 4.9 metres from rest.[c]
- The length of the equator is close to 40000000 m (more precisely 40075014.2 m).[22] In fact, the dimensions of our planet were used by the French Academy in the original definition of the metre.[23]
- The metre is close to the length of a pendulum that has a period of 2 seconds;[d] most dining tabletops are about 0.75 metres high;[24] a very tall human (basketball forward) is about 2 metres tall.[25]
- The kilogram is the mass of a litre of cold water; a cubic centimetre or millilitre of water has a mass of one gram; a 1-euro coin weighs 7.5 g;[26] a Sacagawea US 1-dollar coin weighs 8.1 g;[27] a UK 50-pence coin weighs 8.0 g.[28]
- A candela is about the luminous intensity of a moderately bright candle, or 1 candle power; a 60 W tungsten-filament incandescent light bulb has a luminous intensity of about 64 candelas.[e]
- A mole of a substance has a mass that is its molecular mass expressed in units of grams; the mass of a mole of carbon is 12.0 g, and the mass of a mole of table salt is 58.4 g.
- 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 1/5 oxygen (molecular mass 32) and 4/5 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 4/5 × 28 + 1/5 × 32 = 28.8 ≈ 29). For example, carbon monoxide (molecular mass 28) has almost the same density as air.
- A temperature difference of one kelvin is the same as one degree Celsius: 1/100 of the temperature differential between the freezing and boiling points of water at sea level; the absolute temperature in kelvins is the temperature in degrees Celsius plus about 273; human body temperature is about 37 °C or 310 K.
- A 60 W incandescent light bulb rated at 120 V (US mains voltage) consumes 0.5 A at this voltage. A 60 W bulb rated at 230 V (European mains voltage) consumes 0.26 A at this voltage.[f]
Common metric systems
A number of different metric system 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.
Quantity | MKS
|
CGS | MTS |
---|---|---|---|
distance, length, height, etc. (d, l, h, ...) |
metre (m) |
centimetre (cm) |
metre (m) |
mass (m) |
kilogram (kg) |
gram (g) |
tonne (t) |
time (t) |
second (s) |
second (s) |
second (s) |
speed, velocity (v, v) |
m/s | cm/s | m/s |
acceleration (a) |
m/s2 | gal (Gal) |
m/s2 |
force (F) |
newton (N) | dyne (dyn) |
sthene (sn) |
pressure (P or p) |
pascal (Pa) | barye (Ba) |
pièze (pz) |
energy (E, Q, W) |
joule (J) |
erg (erg) |
kilojoule (kJ) |
power (P) |
watt (W) |
erg/s (erg/s) |
kilowatt (kW) |
viscosity (μ) |
Pa⋅s | poise (P) |
pz⋅s |
19th century
In 1832, Gauss used the astronomical second as a base unit in defining the gravitation of the Earth, and together with the milligram and millimetre, this became
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.[34] 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 107 m (approximately a quadrant of the Earth's circumference), the eleventhgram, equal to 10−11 g, and the second. These were chosen so that the corresponding electrical units of potential difference, current and resistance had a convenient magnitude.[35]: 268 [36]: 17
20th century
In 1901, Giovanni 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.[37][21]
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.[38][39] 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.[40] Although the CGPM passed a resolution in 1901 defining the standard value of acceleration due to gravity to be 980.665 cm/s2, gravitational units are not part of the International System of Units (SI).[41]
International System of Units
The International System of Units is the modern metric system. It is based on the metre–kilogram–second–ampere (MKSA) system of units from early in the 20th century.
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
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 1⁄299,792,458 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–).[43]
See also
- Binary prefix, used in computer science
- Electrostatic units
- History of measurement
- ISO/IEC 80000, international standard of quantities and their units, superseding ISO 31
- List of metric units
- Metrology
- Preferred metric sizes
- Unified Code for Units of Measure
Notes
- ^ Non-SI units for time and plane angle measurement, inherited from existing systems, are an exception to the decimal-multiplier rule.[1]
- ^ While the second is readily determined from the Earth's rotation period, the metre, originally defined in terms of the Earth's size and shape, is less amenable; however, the fact that the Earth's circumference is very close to 40000 km may be a useful mnemonic.
- ^ This is evident from the formula s = v0 t + 1/2 a t2 with v0 = 0 and a = 9.81 m/s2.
- ^ This is evident from the formula T = 2π √L / g.
- ^ A 60 watt light bulb has about 800 lumens[29] which is radiated equally in all directions (i.e. 4π steradians), thus is equal to Iv = 800 lm/4π sr ≈ 64 cd.
- ^ This is evident from the formula P = I V.
References
- ^ "Non-SI units accepted for use with SI". Metric System. 26 July 2018. Retrieved 10 July 2023.
- ^ ISBN 92-822-2213-6, archived(PDF) from the original on 4 June 2021, retrieved 16 December 2021
- ^ ISBN 978-0-948251-84-9.
- ^ "The International System of Units (SI), 9th Edition" (PDF). Bureau International des Poids et Mesures. 2019. Archived (PDF) from the original on 30 May 2019.
- PMID 11861460.
- ^ ISBN 978-1-947172-01-2.
- ISBN 978-0-349-11507-8.
- BIPM. 2011. Retrieved 11 March 2011.
- ^ "OIML Mutual Acceptance Arrangement (MAA)". International Organization of Legal Metrology. Archived from the original on 21 May 2013. Retrieved 23 April 2013.
- ^ "17th General Conference on Weights and Measures (1983), Resolution 1". Retrieved 17 June 2023.
- ^ "Mise en pratique for the definition of the metre in the SI". BIPM. 20 May 2019. Retrieved 17 June 2023.
- ^ Lewis, A. (4 July 2019). 1983 realisation of the metre definition (PDF). Varenna Summer School. National Physical Laboratory. p. 15. Retrieved 10 July 2023.
- ^ "The Latest: Landmark Change to Kilogram Approved". AP News. Associated Press. 16 November 2018. Retrieved 17 June 2023.
- ^ "Mise en pratique for the definition of the kilogram in the SI". BIPM. 7 July 2021. Retrieved 17 June 2023.
- ^ Resnick, Brian (20 May 2019). "The new kilogram just debuted. It's a massive achievement". Vox. Retrieved 17 June 2023.
- ISBN 978-0-393-04002-9.
- ^ Brewster, D. (1830). The Edinburgh Encyclopædia. p. 494.
- ^ Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2). (2008), International vocabulary of metrology – Basic and general concepts and associated terms (VIM) (PDF) (3rd ed.), International Bureau of Weights and Measures (BIPM) on behalf of the Joint Committee for Guides in Metrology, 1.12, retrieved 12 April 2012
{{citation}}
: CS1 maint: numeric names: authors list (link) - ^ Good, Michael. "Some Derivations of E = mc2" (PDF). Archived from the original (PDF) on 7 November 2011. Retrieved 18 March 2011.
- ^ ISBN 92-822-2213-6, archived(PDF) from the original on 4 June 2021, retrieved 16 December 2021
- ^ S2CID 119278961.
- ^ Science, Tim Sharp 2017-09-15T15:47:00Z; Astronomy. "How Big Is Earth?". Space.com. Retrieved 22 October 2019.
{{cite web}}
: CS1 maint: numeric names: authors list (link) - ^ "Metre | measurement". Encyclopedia Britannica. Retrieved 22 October 2019.
- ^ "Standard Table Sizes". Bassett Furniture. Retrieved 22 October 2019.
- ^ "The Average Height of NBA Players – From Point Guards to Centers". The Hoops Geek. 9 December 2018. Retrieved 22 October 2019.
- ^ "RUBINGHSCIENCE.ORG / Using Euro coins as weights". www.rubinghscience.org. Retrieved 22 October 2019.
- ^ "Coin Specifications | U.S. Mint". www.usmint.gov. 20 September 2016. Retrieved 22 October 2019.
- ^ "Fifty Pence Coin". www.royalmint.com. Retrieved 22 October 2019.
- ^ "Lumens and the Lighting Facts Label". Energy.gov. Retrieved 11 June 2020.
- S2CID 145724822.
- ISSN 0002-9505.
- ISBN 92-822-2213-6, archived(PDF) from the original on 4 June 2021, retrieved 16 December 2021
- ^ Thomson, William; Joule, James Prescott; Maxwell, James Clerk; Jenkin, Flemming (1873). "First Report – Cambridge 3 October 1862". In Jenkin, Flemming (ed.). Reports on the Committee on Standards of Electrical Resistance – Appointed by the British Association for the Advancement of Science. London. pp. 1–3. Retrieved 12 May 2011.
{{cite book}}
: CS1 maint: location missing publisher (link) - ^ "Historical context of the SI—Unit of electric current (ampere)". The NIST Reference on Constants, Units and Uncertainty. Retrieved 10 April 2011.
- ^ James Clerk Maxwell (1954) [1891], A Treatise on Electricity & Magnetism, vol. 2 (3rd ed.), Dover Publications
- arXiv:1506.01951 [physics.hist-ph].
- ^ "In the beginning... Giovanni Giorgi". International Electrotechnical Commission. 2011. Archived from the original on 15 May 2011. Retrieved 5 April 2011.
- ^ "System of Measurement Units". IEEE Global History Network. Institute of Electrical and Electronics Engineers (IEEE). Retrieved 21 March 2011.
- ^ "Notions de physique – Systèmes d'unités" [Symbols used in physics – units of measure] (in French). Hydrelect.info. Retrieved 21 March 2011.
- ^ Michon, Gérard P (9 September 2000). "Final Answers". Numericana.com. Retrieved 11 October 2012.
- ^ "Resolution of the 3rd meeting of the CGPM (1901)". General Conference on Weights and Measures. Retrieved 11 October 2012.
- S2CID 241546445.
- ^ "New SI prefixes clear the way for quettabytes of storage". The Register. 22 November 2022. Retrieved 23 November 2022.
External links
- Learning materials related to Using the Metric System at Wikiversity