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| {{Redirect|Unit of measure}}
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| {{Redirect|Weights and measures}}
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| [[Image:Weights and Measures office.jpg|thumb|upright=1.5|right|The former Weights and Measures office in [[Seven Sisters, London]]]]
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| [[File:Unità di misura - Palazzo della Ragione - Padova.jpg|thumb|upright=1.5|right|Units of measurement, [[Palazzo della Ragione]], [[Padua]]]]
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| A '''unit of measurement''' is a definite [[magnitude (mathematics)|magnitude]] of a [[physical quantity]], defined and adopted by convention or by law, that is used as a standard for measurement of the same physical quantity.<ref>{{VIM3rd|term=measurement unit|pages=6–7}}.</ref> Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement.
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| For example, [[length]] is a physical quantity. The [[metre]] is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre".
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| The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different [[System of measurement|systems of units]] used to be very common. Now there is a global standard, the [[International System of Units]] (SI), the modern form of the [[metric system]].
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| In trade, '''weights and measures''' is often a subject of governmental regulation, to ensure fairness and transparency. The [[International Bureau of Weights and Measures]] (BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the International System of Units (SI). [[Metrology]] is the science for developing nationally and internationally accepted units of weights and measures.
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| In [[physics]] and [[metrology]], units are standards for [[measurement]] of [[physical quantity|physical quantities]] that need clear definitions to be useful. [[Reproducibility]] of experimental results is central to the [[scientific method]]. A standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights and measures developed long ago for commercial purposes.
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| [[Science]], [[medicine]], and [[engineering]] often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measurement can aid researchers in [[problem solving]] (see, for example, [[dimensional analysis]]).
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| In the [[social sciences]], there are no standard units of measurement and the theory and practice of measurement is studied in [[psychometrics]] and the [[theory of conjoint measurement]].
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| ==History==
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| {{main|History of measurement}}
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| A unit of measurement is a standardised [[quantity]] of a physical property, used as a factor to express occurring quantities of that property. Units of measurement were among the earliest tools invented by humans. Primitive societies needed rudimentary measures for many tasks: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials.
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| The earliest known uniform systems of weights and measures seem to have all been created sometime in the [[4th millennium BC|4th]] and [[3rd millennium BC|3rd millennia BC]] among the ancient peoples of [[Mesopotamia]], [[Ancient Egypt|Egypt]] and the [[Indus Valley Civilization|Indus Valley]], and perhaps also [[Elam]] in [[Iran|Persia]] as well.
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| Weights and measures are mentioned in the Bible (Leviticus 19:35-36). It is a commandment to be honest and have fair measures.
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| In "The [[Magna Carta]]" of 1215 (The Great Charter) with the seal of [[John, King of England|King John]], put before him by the Barons of England, King John agreed in Clause 35 "There shall be one measure of wine throughout our whole realm, and one measure of ale and one measure of corn--namely, the London quart;--and one width of dyed and russet and hauberk cloths--namely, two ells below the selvage..."<ref>[http://www.frauncestavernmuseum.org/magna_carta/MCFF-Education-Packet.pdf ]{{dead link|date=June 2012}}</ref>
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| Many systems were based on the use of parts of the body and the natural surroundings as measuring instruments. Our present knowledge of early weights and measures comes from many sources.
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| ==Systems of units==
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| {{main|System of measurement}}
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| ===Traditional systems===
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| Historically many of the systems of measurement which had been in use were to some extent based on the dimensions of the human body according to the proportions described by [[Marcus Vitruvius Pollio]].{{citation needed|date=December 2011}} As a result, units of measure could vary not only from location to location, but from person to person.
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| ===Metric systems===
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| A number of [[metric system]]s of units have [[History of the metric system|evolved since the adoption of the original metric system]] in [[France]] in 1791. The current international standard metric system is the [[SI|International System of Units]]. An important feature of modern systems is [[standardization]]. Each unit has a universally recognized size.
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| Both the [[Imperial unit]]s and [[US customary units]] derive from earlier [[English unit]]s. Imperial units were mostly used in the [[Commonwealth of Nations|British Commonwealth]] and the former [[British Empire]]. US customary units are still the main system of measurement used in the [[United States]] despite Congress having legally authorized metric measure on 28 July 1866.<ref>
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| {{cite web
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| |url=http://lamar.colostate.edu/~hillger/laws/metric-act.html
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| |title=US Metric Act of 1866
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| }} as amended by Public Law 110–69 dated August 9, 2007</ref> Some steps towards US [[metrication]] have been made, particularly the redefinition of basic US and imperial units to derive exactly from SI units. Since the [[international yard and pound]] agreement of 1959 the US and imperial inch is now defined as exactly 0.0254 m, and the US and imperial avoirdupois pound is now defined as exactly 453.59237 g.<ref>
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| {{cite web
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| |url=http://ts.nist.gov/WeightsAndMeasures/h44-04.cfm
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| |title=NIST Handbook 44 Appendix B
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| |year=2002
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| |publisher=[[National Institute of Standards and Technology]]
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| }}</ref>
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| ===Natural systems===
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| While the above systems of units are based on arbitrary unit values, formalised as standards, some unit values occur naturally in science. Systems of units based on these are called [[natural units]]. Similar to natural units, [[atomic units]] (au) are a convenient [[system of units]] of measurement used in [[atomic physics]].
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| Also a great number of [[List of unusual units of measurement|unusual]] and non-standard units may be encountered. These may include the [[Solar mass]] (2 x 10<sup>30</sup> kg) and the [[TNT equivalent|Megaton]] (1,000,000 tons of [[Trinitrotoluene|TNT]]).
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| ===Legal control of weights and measures===
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| {{Main|Weights and Measures Act|Trading standards}}
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| To reduce the incidence of retail fraud, many national [[statutes]] have standard definitions of weights and measures that may be used (hence "statute measure"), and these are verified by legal officers.
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| ==Base and derived units==<!-- This section is linked from [[Measurement]] -->
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| Different systems of units are based on different choices of a set of [[fundamental unit]]s.
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| The most widely used system of units is the International System of Units, or [[SI]]. There are seven [[SI base unit]]s. All [[SI derived unit|other SI units]] can be derived from these base units.
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| For most quantities a unit is absolutely necessary to communicate values of that physical quantity. For example, conveying to someone a particular length without using some sort of unit is impossible, because a length cannot be described without a reference used to make sense of the value given.
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| But not all quantities require a unit of their own. Using physical laws, units of quantities can be expressed as combinations of units of other quantities. Thus only a small set of units is required. These units are taken as the ''base units''. Other units are ''derived units''. Derived units are a matter of convenience, as they can be expressed in terms of basic units. Which units are considered base units is a matter of choice.
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| The base units of SI are actually not the smallest set possible. Smaller sets have been defined. For example, there are unit sets{{Which|date=February 2011}} in which the [[electric field|electric]] and [[magnetic field]] have the same unit. This is based on physical laws that show that electric and magnetic field are actually different manifestations of the same phenomenon.
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| ==Calculations with units of measurements==
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| {{howto|section|date=December 2011}}
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| {{merge-from|Units conversion by factor-label|date=June 2013|section=yes}}
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| {{merge-from|Conversion factor|date=June 2013|section=yes}}
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| ===Units as dimensions===
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| Any value of a [[physical quantity]] is expressed as a comparison to a unit of that quantity. For example, the value of a physical quantity ''Z'' is expressed as the product of a unit [Z] and a numerical factor:
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| :<math>Z = n \times [Z] = n [Z].</math> For example, "2 candlesticks" Z = 2 [candlestick].
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| The multiplication sign is usually left out, just as it is left out between variables in scientific notation of formulas. The conventions used to express quantities is referred to as [[quantity calculus]]. In formulas the unit [Z] can be treated as if it were a specific magnitude of a kind of physical [[dimension]]: see [[dimensional analysis]] for more on this treatment.
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| Units can only be added or subtracted if they are the same type; however units can always be multiplied or divided, as [[George Gamow]] used to explain:
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| :"2 candlesticks" times "3 cabdrivers" = 6 [candlestick][cabdriver].
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| A distinction should be made between units and standards. A unit is fixed by its definition, and is independent of physical conditions such as temperature. By contrast, a standard is a physical realization of a unit, and realizes that unit only under certain physical conditions. For example, the metre is a unit, while a metal bar is a standard. One metre is the same length regardless of temperature, but a metal bar will be exactly one metre long only at a certain temperature.
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| ===Guidelines===
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| * Treat units algebraically. Only add like terms. When a unit is divided by itself, the division yields a unitless one. When two different units are multiplied, the result is a new unit, referred to by the combination of the units. For instance, in SI, the unit of speed is metres per second (m/s). See [[dimensional analysis]]. A unit can be multiplied by itself, creating a unit with an exponent (e.g. m<sup>2</sup>/s<sup>2</sup>). Put simply, units obey the laws of indices. (See [[Exponentiation]].)
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| * Some units have special names, however these should be treated like their equivalents. For example, one newton (N) is equivalent to one kg·m/s<sup>2</sup>. Thus a quantity may have several unit designations, for example: the unit for [[surface tension]] can be referred to as either N/m (newtons per metre) or kg/s<sup>2</sup> (kilograms per second squared). Whether these designations are equivalent is disputed amongst metrologists.<ref name="Emerson">{{Cite journal | title = On quantity calculus and units of measurement | first = W.H. | last = Emerson | year = 2008 |journal = [[Metrologia]] | volume = 45 | pages = 134–138 |bibcode = 2008Metro..45..134E |doi = 10.1088/0026-1394/45/2/002 | issue = 2}}</ref>
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| ===Expressing a physical value in terms of another unit===<!-- This section is linked from [[Watt-hour]] -->
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| [[Conversion of units]] involves comparison of different standard physical values, either of a single physical quantity or of a physical quantity and a combination of other physical quantities.
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| Starting with:
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| :<math>Z = n_i \times [Z]_i</math>
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| just replace the original unit <math>[Z]_i</math> with its meaning in terms of the desired unit <math>[Z]_j</math>, e.g. if <math>[Z]_i = c_{ij} \times [Z]_j</math>, then:
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| :<math>Z = n_i \times (c_{ij} \times [Z]_j) = (n_i \times c_{ij}) \times [Z]_j</math>
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| Now <math>n_i</math> and <math>c_{ij}</math> are both numerical values, so just calculate their product.
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| Or, which is just mathematically the same thing, multiply ''Z'' by unity, the product is still ''Z'':
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| :<math>Z = n_i \times [Z]_i \times ( c_{ij} \times [Z]_j/[Z]_i )</math>
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| For example, you have an expression for a physical value ''Z'' involving the unit ''feet per second'' (<math>[Z]_i</math>) and you want it in terms of the unit ''miles per hour'' (<math>[Z]_j</math>):
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| {{ordered list
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| |1= Find facts relating the original unit to the desired unit:
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| :1 mile = 5280 feet and 1 hour = 3600 seconds
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| |2= Next use the above equations to construct a fraction that has a value of unity and that contains units such that, when it is multiplied with the original physical value, will cancel the original units:
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| :<math>1 = \frac{1\,\mathrm{mi}}{5280\,\mathrm{ft}}\quad \mathrm{and}\quad 1 = \frac{3600\,\mathrm{s}}{1\,\mathrm{h}}</math>
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| |3= Last, multiply the original expression of the physical value by the fraction, called a ''[[conversion factor]]'', to obtain the same physical value expressed in terms of a different unit. Note: since valid conversion factors are [[dimensionless]] and have a numerical value of [[one]], multiplying any physical quantity by such a conversion factor (which is 1) does not change that physical quantity.
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| :<math> 52.8\,\frac{\mathrm{ft}}{\mathrm{s}} =
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| 52.8\,\frac{\mathrm{ft}}{\mathrm{s}}
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| \frac{1\,\mathrm{mi}}{5280\,\mathrm{ft}}
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| \frac{3600\,\mathrm{s}}{1\,\mathrm{h}} =
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| \frac {52.8 \times 3600}{5280}\,\mathrm{mi/h}
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| = 36\,\mathrm{mi/h}</math>
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| }}
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| Or as an example using the metric system, you have a value of fuel economy in the unit ''litres per 100 kilometres'' and you want it in terms of the unit ''microlitres per metre'':
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| :<math> \mathrm{\frac{9\,\rm{L}}{100\,\rm{km}}} =
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| \mathrm{\frac{9\,\rm{L}}{100\,\rm{km}}}
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| \mathrm{\frac{1000000\,\rm{\mu L}}{1\,\rm{L}}}
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| \mathrm{\frac{1\,\rm{km}}{1000\,\rm{m}}} =
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| \frac {9 \times 1000000}{100 \times 1000}\,\mathrm{\mu L/m} =
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| 90\,\mathrm{\mu L/m}</math>
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| ==Real-world implications==
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| One example of the importance of agreed units is the failure of the [[NASA]] [[Mars Climate Orbiter]], which was accidentally destroyed on a mission to Mars in September 1999 instead of entering orbit due to miscommunications about the value of forces: different computer programs used different units of measurement ([[Newton (unit)|newton]] versus [[pound force]]). Considerable amounts of effort, time, and money were wasted.<ref name=mixups>
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| {{cite web
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| |url=http://lamar.colostate.edu/~hillger/unit-mixups.html
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| |title=Unit Mixups
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| |publisher=US Metric Association
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| }}</ref><ref>
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| {{cite web
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| |url=ftp://ftp.hq.nasa.gov/pub/pao/reports/1999/MCO_report.pdf
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| |publisher=NASA
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| |date=1999-11-10
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| |title=Mars Climate Orbiter Mishap Investigation Board Phase I Report
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| }}</ref>
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| On April 15, 1999 [[Korean Air]] cargo {{link-zh|Korean Air Cargo Flight 6316|大韓航空6316號班機空難|flight 6316}} from [[Shanghai]] to [[Seoul]] was lost due to the crew confusing tower instructions (in metres) and altimeter readings (in feet). Three crew and five people on the ground were killed. Thirty seven were injured.<ref>
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| {{cite press release
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| |url=http://www.ntsb.gov/pressrel/1999/990427.htm
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| |title=Korean Air Flight 6316
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| |publisher=[[NTSB]]
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| }}</ref><ref>
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| {{cite web
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| |url=http://aviation-safety.net/database/record.php?id=19990415-0
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| |title=Korean Air incident
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| |publisher=Aviation Safety Net
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| }}</ref>
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| In 1983, a Boeing 767 (which came to be known as the [[Gimli Glider]]) ran out of fuel in mid-flight because of two mistakes in figuring the fuel supply of [[Air Canada]]'s first aircraft to use metric measurements.<ref>
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| {{cite news
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| |first=Richard
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| |last=Witkin
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| |authorlink=
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| |coauthors=
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| |title=Jet's Fuel Ran Out After Metric Conversion Errors
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| |url=http://select.nytimes.com/search/restricted/article?res=F00F17F73B5D0C738FDDAE0894DB484D81
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| |quote=Air Canada said yesterday that its Boeing 767 jet ran out of fuel in mid-flight last week because of two mistakes in figuring the fuel supply of the airline's first aircraft to use metric measurements. After both engines lost their power, the pilots made what is now thought to be the first successful emergency ''dead stick'' landing of a commercial jetliner.
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| |publisher=New York Times
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| |date=July 30, 1983
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| |accessdate=2007-08-21
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| }}</ref> This accident is apparently the result of confusion both due to the simultaneous use of metric & Imperial measures as well as mass & volume measures.
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| ==See also==
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| {{multicol}}
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| * [[Chinese units of measurement]]
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| * [[Indian weights and measures]]
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| * [[Japanese units of measurement]]
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| * [[List of humorous units of measurement]]
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| * [[List of unusual units of measurement]]
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| {{multicol-break}}
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| * [[Spanish customary units]]
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| * [[Taiwanese units of measurement]]
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| * [[Unified Code for Units of Measure]]
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| * [[United States customary units]]
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| * [[Units conversion by factor-label]]
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| {{multicol-end}}
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| ==Notes==
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| {{Reflist|30em}}
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| ==External links==
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| * Rowlett, Russ (2005) [http://www.unc.edu/~rowlett/units/ A Dictionary of Units of Measurement] - Russ Rowlett and the University of North Carolina at Chapel Hill
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| * [http://ts.nist.gov/WeightsAndMeasures/Publications/H44-09.cfm NIST Handbook 44], ''Specifications, Tolerances, and Other Technical Requirements for Weighing and Measuring Devices''
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| * [http://www.bipm.org/en/si Official SI website]
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| * [http://QuantitySystem.CodePlex.com/ Quantity System Framework] - Quantity System Library and Calculator for Units Conversions and Quantities predictions
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| ===Historical===
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| *[http://www.wdl.org/en/item/2847 "Arithmetic Conventions for Conversion Between Roman [i.e. Ottoman] and Egyptian Measurement"] is a manuscript from 1642, in Arabic, which is about units of measurement.
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| ===Legal===
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| * [http://www.irishstatutebook.ie/1996/en/act/pub/0027/ Ireland - Metrology Act 1996]
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| * [http://www.law.cornell.edu/uscode/search/display.html?terms=unit%20measure&url=/uscode/html/uscode15/usc_sec_15_00000205----000-notes.html US - Authorized tables ]
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| * {{UK-LEG|type=uksi|path=uksi/1995/1804|title=Units of Measurement Regulations 1995}}
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| ===Metric information and associations===
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| * [http://www.bipm.org/en/si BIPM] (official site)
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| * [http://www.ukma.org.uk/ UK Metric Association]
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| * [http://lamar.colostate.edu/~hillger US Metric Association]
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| * [http://unitsofmeasure.org/ The Unified Code for Units of Measure] (UCUM)
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| ===Imperial measure information===
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| * [http://www.bwmaonline.com/ British Weights and Measures Association]
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| {{systems of measurement}}
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| {{DEFAULTSORT:Units Of Measurement}}
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| [[Category:Units of measurement|*]]
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| [[Category:Customary units of measurement|*]]
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| [[Category:Human-based units of measurement|*]]
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| [[Category:Measurement]]
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| [[Category:Obsolete units of measurement|*]]
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| [[Category:Systems of units|*]]
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