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98-592: In metrology ( International System of Quantities and the International System of Units ), "quotient" refers to the general case with respect to the units of measurement of physical quantities . Ratios is the special case for dimensionless quotients of two quantities of the same kind . Quotients with a non-trivial dimension and compound units , especially when the divisor is a duration (e.g., " per second "), are known as rates . For example, density (mass divided by volume, in units of kg/m )

196-401: A set with an equivalence relation defined on it, a " quotient set " may be created which contains those equivalence classes as elements. A quotient group may be formed by breaking a group into a number of similar cosets , while a quotient space may be formed in a similar process by breaking a vector space into a number of similar linear subspaces . Metrology Metrology

294-482: A 95% confidence that the measured value will fall inside the uncertainty interval. Other values of k can be used to indicate a greater or lower confidence on the interval, for example k = 1 and k = 3 generally indicate 66% and 99.7% confidence respectively. The uncertainty value is determined through a combination of statistical analysis of the calibration and uncertainty contribution from other errors in measurement process, which can be evaluated from sources such as

392-669: A CIPM report and endorse new developments in the SI as advised by the CIPM. The last meeting was held on 13–16 November 2018. On the last day of this conference there was vote on the redefinition of four base units, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year. The new definitions came into force on 20 May 2019. The International Committee for Weights and Measures ( French : Comité international des poids et mesures , or CIPM)

490-481: A comparison framework. The system defines seven fundamental units : kilogram , metre , candela , second , ampere , kelvin , and mole . All of these units are defined without reference to a particular physical object which serves as a standard. Artifact-free definitions fix measurements at an exact value related to a physical constant or other invariable phenomena in nature, in contrast to standard artifacts which are subject to deterioration or destruction. Instead,

588-480: A conference in 1977 to develop international cooperation for accredited testing and calibration results to facilitate trade. In 2000, 36 members signed the ILAC mutual recognition agreement (MRA), allowing members work to be automatically accepted by other signatories, and in 2012 was expanded to include accreditation of inspection bodies. Through this standardisation, work done in laboratories accredited by signatories

686-580: A country's accreditation body must comply with international requirements and is generally the product of international and regional cooperation. A laboratory is evaluated according to international standards such as ISO/IEC 17025 general requirements for the competence of testing and calibration laboratories. To ensure objective and technically-credible accreditation, the bodies are independent of other national measurement system institutions. The National Association of Testing Authorities in Australia and

784-503: A country's measurement infrastructure. The NMS sets measurement standards, ensuring the accuracy, consistency, comparability, and reliability of measurements made in the country. The measurements of member countries of the CIPM Mutual Recognition Arrangement (CIPM MRA), an agreement of national metrology institutes, are recognized by other member countries. As of March 2018, there are 102 signatories of

882-458: A digital read-out, but require a gravitational field to function and would not work in free fall. The measures used in economics are physical measures, nominal price value measures and real price measures. These measures differ from one another by the variables they measure and by the variables excluded from measurements. In the field of survey research, measures are taken from individual attitudes, values, and behavior using questionnaires as

980-522: A distance of one metre (about 39  in ). Using physics, it can be shown that, in the gravitational field of the Earth, it should take any object about 0.45 second to fall one metre. However, the following are just some of the sources of error that arise: Additionally, other sources of experimental error include: Scientific experiments must be carried out with great care to eliminate as much error as possible, and to keep error estimates realistic. In

1078-460: A few examples. Imperial units are used in many other places, for example, in many Commonwealth countries that are considered metricated, land area is measured in acres and floor space in square feet, particularly for commercial transactions (rather than government statistics). Similarly, gasoline is sold by the gallon in many countries that are considered metricated. The metric system is a decimal system of measurement based on its units for length,

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1176-440: A filter, changing the quantum state into one with the single measured quantum value. The unambiguous meaning of the quantum measurement is an unresolved fundamental problem in quantum mechanics ; the most common interpretation is that when a measurement is performed, the wavefunction of the quantum system " collapses " to a single, definite value. In biology, there is generally no well established theory of measurement. However,

1274-646: A kilogram without an artefact the value of the Planck constant must be known to twenty parts per billion. Scientific metrology, through the development of the Kibble balance and the Avogadro project , has produced a value of Planck constant with low enough uncertainty to allow for a redefinition of the kilogram. Applied, technical or industrial metrology is concerned with the application of measurement to manufacturing and other processes and their use in society, ensuring

1372-1082: A lead NMI and several decentralised institutes specialising in specific national standards. Some examples of NMI's are the National Institute of Standards and Technology (NIST) in the United States, the National Research Council (NRC) in Canada, the Physikalisch-Technische Bundesanstalt (PTB) in Germany, and the National Physical Laboratory (United Kingdom) (NPL). Calibration laboratories are generally responsible for calibrations of industrial instrumentation. Calibration laboratories are accredited and provide calibration services to industry firms, which provides

1470-420: A measurement instrument. As all other measurements, measurement in survey research is also vulnerable to measurement error , i.e. the departure from the true value of the measurement and the value provided using the measurement instrument. In substantive survey research, measurement error can lead to biased conclusions and wrongly estimated effects. In order to get accurate results, when measurement errors appear,

1568-409: A measurement is an action that determines a particular property (position, momentum, energy, etc.) of a quantum system. Quantum measurements are always statistical samples from a probability distribution; the distribution for many quantum phenomena is discrete. Quantum measurements alter quantum states and yet repeated measurements on a quantum state are reproducible. The measurement appears to act as

1666-503: A mutual acceptance arrangement (MAA) for measuring instruments that are subject to legal metrological control, which upon approval allows the evaluation and test reports of the instrument to be accepted in all participating countries. Issuing participants in the agreement issue MAA Type Evaluation Reports of MAA Certificates upon demonstration of compliance with ISO/IEC 17065 and a peer evaluation system to determine competency. This ensures that certification of measuring devices in one country

1764-465: A national measurement system to be recognized internationally by the CIPM Mutual Recognition Arrangement, an NMI must participate in international comparisons of its measurement capabilities. BIPM maintains a comparison database and a list of calibration and measurement capabilities (CMCs) of the countries participating in the CIPM MRA. Not all countries have a centralised metrology institute; some have

1862-588: A positive impact on GDP . In the United Kingdom, an estimated 28.4 per cent of GDP growth from 1921 to 2013 was the result of standardisation; in Canada between 1981 and 2004 an estimated nine per cent of GDP growth was standardisation-related, and in Germany the annual economic benefit of standardisation is an estimated 0.72% of GDP. Legal metrology has reduced accidental deaths and injuries with measuring devices, such as radar guns and breathalyzers , by improving their efficiency and reliability. Measuring

1960-685: A scientific basis, overseen by governmental or independent agencies, and established in international treaties, pre-eminent of which is the General Conference on Weights and Measures (CGPM), established in 1875 by the Metre Convention , overseeing the International System of Units (SI). For example, the metre was redefined in 1983 by the CGPM in terms of the speed of light, the kilogram was redefined in 2019 in terms of

2058-455: A technical infrastructure and tools that can then be used to pursue further innovation. By providing a technical platform which new ideas can be built upon, easily demonstrated, and shared, measurement standards allow new ideas to be explored and expanded upon. Measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement

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2156-402: A traceability link back to the national metrology institute. Since the calibration laboratories are accredited, they give companies a traceability link to national metrology standards. An organisation is accredited when an authoritative body determines, by assessing the organisation's personnel and management systems, that it is competent to provide its services. For international recognition,

2254-576: Is a collaboration of eight partner organisations: The JCGM has two working groups: JCGM-WG1 and JCGM-WG2. JCGM-WG1 is responsible for the GUM, and JCGM-WG2 for the VIM. Each member organization appoints one representative and up to two experts to attend each meeting, and may appoint up to three experts for each working group. A national measurement system (NMS) is a network of laboratories, calibration facilities and accreditation bodies which implement and maintain

2352-493: Is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering , measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by

2450-400: Is also less commonly defined as the greatest whole number of times a divisor may be subtracted from a dividend—before making the remainder negative. For example, the divisor 3 may be subtracted up to 6 times from the dividend 20, before the remainder becomes negative: while In this sense, a quotient is the integer part of the ratio of two numbers. A rational number can be defined as

2548-510: Is an apparently irreversible series of occurrences within this non spatial continuum. It is also used to denote an interval between two relative points on this continuum. Mass refers to the intrinsic property of all material objects to resist changes in their momentum. Weight , on the other hand, refers to the downward force produced when a mass is in a gravitational field. In free fall , (no net gravitational forces) objects lack weight but retain their mass. The Imperial units of mass include

2646-454: Is an organisation based in Sèvres, France which has custody of the international prototype of the kilogram , provides metrology services for the CGPM and CIPM, houses the secretariat for the organisations and hosts their meetings. Over the years, prototypes of the metre and of the kilogram have been returned to BIPM headquarters for recalibration. The BIPM director is an ex officio member of

2744-635: Is automatically recognised internationally through the MRA. Other work done by ILAC includes promotion of laboratory and inspection body accreditation, and supporting the development of accreditation systems in developing economies. The Joint Committee for Guides in Metrology (JCGM) is a committee which created and maintains two metrology guides: Guide to the expression of uncertainty in measurement (GUM) and International vocabulary of metrology – basic and general concepts and associated terms (VIM). The JCGM

2842-604: Is compatible with another country's certification process, allowing the trade of the measuring devices and the products that rely on them. WELMEC was established in 1990 to promote cooperation in the field of legal metrology in the European Union and among European Free Trade Association (EFTA) member states. In the United States legal metrology is under the authority of the Office of Weights and Measures of National Institute of Standards and Technology (NIST), enforced by

2940-542: Is compatible with the certification process in other participating countries, allowing the trade of the measuring devices and the products that rely on them. The International Laboratory Accreditation Cooperation (ILAC) is an international organisation for accreditation agencies involved in the certification of conformity-assessment bodies. It standardises accreditation practices and procedures, recognising competent calibration facilities and assisting countries developing their own accreditation bodies. ILAC originally began as

3038-420: Is defined as the "property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty". It permits the comparison of measurements, whether the result is compared to the previous result in the same laboratory, a measurement result a year ago, or to the result of a measurement performed anywhere else in

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3136-533: Is defined by the International Bureau of Weights and Measures (BIPM) as "the science of measurement, embracing both experimental and theoretical determinations at any level of uncertainty in any field of science and technology". It establishes a common understanding of units, crucial to human activity. Metrology is a wide reaching field, but can be summarized through three basic activities: the definition of internationally accepted units of measurement,

3234-513: Is made up of eighteen (originally fourteen) individuals from a member state of high scientific standing, nominated by the CGPM to advise the CGPM on administrative and technical matters. It is responsible for ten consultative committees (CCs), each of which investigates a different aspect of metrology; one CC discusses the measurement of temperature, another the measurement of mass, and so forth. The CIPM meets annually in Sèvres to discuss reports from

3332-413: Is pursued in the field of metrology . Measurement is defined as the process of comparison of an unknown quantity with a known or standard quantity. The measurement of a property may be categorized by the following criteria: type , magnitude , unit , and uncertainty . They enable unambiguous comparisons between measurements. Measurements most commonly use the International System of Units (SI) as

3430-402: Is quantitative if such structural similarities can be established. In weaker forms of representational theory, such as that implicit within the work of Stanley Smith Stevens , numbers need only be assigned according to a rule. The concept of measurement is often misunderstood as merely the assignment of a value, but it is possible to assign a value in a way that is not a measurement in terms of

3528-455: Is said to be a "quotient", whereas mass fraction (mass divided by mass, in kg/kg or in percent) is a "ratio". Specific quantities are intensive quantities resulting from the quotient of a physical quantity by mass, volume, or other measures of the system "size". The quotient is most frequently encountered as two numbers, or two variables, divided by a horizontal line. The words "dividend" and "divisor" refer to each individual part, while

3626-563: Is the international standards, which beholds the world's standards. The next level is the national Metrology institutes that have primary standards that are traceable to the international standards. The national Metrology institutes standards are used to establish a traceable link to local laboratory standards, these laboratory standards are then used to establish a traceable link to industry and testing laboratories. Through these subsequent calibrations between national metrology institutes, calibration laboratories, and industry and testing laboratories

3724-593: Is the scientific study of measurement . It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution 's political motivation to standardise units in France when a length standard taken from a natural source was proposed. This led to the creation of the decimal-based metric system in 1795, establishing a set of standards for other types of measurements. Several other countries adopted

3822-427: Is to fall within the uncertainty interval. Uncertainty is generally expressed as follows: Where y is the measurement value and U is the uncertainty value and k is the coverage factor indicates the confidence interval. The upper and lower limit of the uncertainty interval can be determined by adding and subtracting the uncertainty value from the measurement value. The coverage factor of k = 2 generally indicates

3920-538: The Commonwealth and the United States. The system came to be known as U.S. customary units in the United States and is still in use there and in a few Caribbean countries. These various systems of measurement have at times been called foot-pound-second systems after the Imperial units for length, weight and time even though the tons, hundredweights, gallons, and nautical miles, for example, are different for

4018-488: The French language name Système International d'Unités ) is the modern revision of the metric system . It is the world's most widely used system of units , both in everyday commerce and in science . The SI was developed in 1960 from the metre–kilogram–second (MKS) system, rather than the centimetre–gram–second (CGS) system, which, in turn, had many variants. The SI units for the seven base physical quantities are: In

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4116-498: The International Bureau of Weights and Measures . However, in other fields such as statistics as well as the social and behavioural sciences , measurements can have multiple levels , which would include nominal, ordinal, interval and ratio scales. Measurement is a cornerstone of trade , science , technology and quantitative research in many disciplines. Historically, many measurement systems existed for

4214-828: The National Physical Laboratory (NPL), in Australia by the National Measurement Institute , in South Africa by the Council for Scientific and Industrial Research and in India the National Physical Laboratory of India . unit is known or standard quantity in terms of which other physical quantities are measured. Before SI units were widely adopted around the world, the British systems of English units and later imperial units were used in Britain,

4312-550: The Planck constant ( h ), the elementary electric charge ( e ), the Boltzmann constant ( k ), and the Avogadro constant ( N A ), respectively. The second , metre , and candela have previously been defined by physical constants (the caesium standard (Δ ν Cs ), the speed of light ( c ), and the luminous efficacy of 540 × 10  Hz visible light radiation ( K cd )), subject to correction to their present definitions. The new definitions aim to improve

4410-557: The Planck constant and the international yard was defined in 1960 by the governments of the United States, United Kingdom, Australia and South Africa as being exactly 0.9144 metres. In the United States, the National Institute of Standards and Technology ( NIST ), a division of the United States Department of Commerce , regulates commercial measurements. In the United Kingdom, the role is performed by

4508-672: The United Kingdom Accreditation Service are examples of accreditation bodies. Metrology has wide-ranging impacts on a number of sectors, including economics, energy, the environment, health, manufacturing, industry, and consumer confidence. The effects of metrology on trade and the economy are two of its most-apparent societal impacts. To facilitate fair and accurate trade between countries, there must be an agreed-upon system of measurement. Accurate measurement and regulation of water, fuel, food, and electricity are critical for consumer protection and promote

4606-403: The ounce , pound , and ton . The metric units gram and kilogram are units of mass. One device for measuring weight or mass is called a weighing scale or, often, simply a scale . A spring scale measures force but not mass, a balance compares weight, both require a gravitational field to operate. Some of the most accurate instruments for measuring weight or mass are based on load cells with

4704-459: The quantum Hall effect for the ohm ), and the use of a material object as the measurement standard. A standard (or etalon) is an object, system, or experiment with a defined relationship to a unit of measurement of a physical quantity. Standards are the fundamental reference for a system of weights and measures by realising, preserving, or reproducing a unit against which measuring devices can be compared. There are three levels of standards in

4802-479: The ruler is the instrument used to rule straight lines and the calibrated instrument used for determining length is called a measure , however common usage calls both instruments rulers and the special name straightedge is used for an unmarked rule. The use of the word measure , in the sense of a measuring instrument, only survives in the phrase tape measure , an instrument that can be used to measure but cannot be used to draw straight lines. As can be seen in

4900-505: The steelyard balance and other tools. Other civilizations produced generally accepted measurement standards, with Roman and Greek architecture based on distinct systems of measurement. The collapse of the empires and the Dark Ages that followed lost much measurement knowledge and standardisation. Although local systems of measurement were common, comparability was difficult since many local systems were incompatible. England established

4998-452: The Assize of Measures to create standards for length measurements in 1196, and the 1215 Magna Carta included a section for the measurement of wine and beer. Modern metrology has its roots in the French Revolution . With a political motivation to harmonise units throughout France, a length standard based on a natural source was proposed. In March 1791, the metre was defined. This led to

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5096-467: The BIPM to complete the task of defining all SI base units in terms of physical constants . By defining SI base units with respect to physical constants, and not artefacts or specific substances, they are realisable with a higher level of precision and reproducibility. As of the revision of the SI on 20 May 2019 the kilogram , ampere , kelvin , and mole are defined by setting exact numerical values for

5194-506: The CCs, to submit an annual report to the governments of member states concerning the administration and finances of the BIPM and to advise the CGPM on technical matters as needed. Each member of the CIPM is from a different member state, with France (in recognition of its role in establishing the convention) always having one seat. The International Bureau of Weights and Measures ( French : Bureau international des poids et mesures , or BIPM)

5292-402: The CIPM MRA, consisting of 58 member states, 40 associate states, and 4 international organizations. A national metrology institute's (NMI) role in a country's measurement system is to conduct scientific metrology, realise base units, and maintain primary national standards. An NMI provides traceability to international standards for a country, anchoring its national calibration hierarchy. For

5390-485: The CIPM and a member of all consultative committees. The International Organization of Legal Metrology ( French : Organisation Internationale de Métrologie Légale , or OIML), is an intergovernmental organization created in 1955 to promote the global harmonisation of the legal metrology procedures facilitating international trade. This harmonisation of technical requirements, test procedures and test-report formats ensure confidence in measurements for trade and reduces

5488-672: The International Committee for Weights and Measures (CIPM), was an advisory committee of metrologists of high standing. The third, the International Bureau of Weights and Measures (BIPM), provided secretarial and laboratory facilities for the CGPM and CIPM. The General Conference on Weights and Measures ( French : Conférence générale des poids et mesures , or CGPM) is the convention's principal decision-making body, consisting of delegates from member states and non-voting observers from associate states. The conference usually meets every four to six years to receive and discuss

5586-415: The SI without changing the size of any units, thus ensuring continuity with existing measurements. The realisation of a unit of measure is its conversion into reality. Three possible methods of realisation are defined by the international vocabulary of metrology (VIM): a physical realisation of the unit from its definition, a highly-reproducible measurement as a reproduction of the definition (such as

5684-464: The SI, base units are the simple measurements for time, length, mass, temperature, amount of substance, electric current and light intensity. Derived units are constructed from the base units, for example, the watt , i.e. the unit for power, is defined from the base units as m ·kg·s . Other physical properties may be measured in compound units, such as material density, measured in kg/m . The SI allows easy multiplication when switching among units having

5782-405: The U.S. units. Many Imperial units remain in use in Britain, which has officially switched to the SI system—with a few exceptions such as road signs, which are still in miles. Draught beer and cider must be sold by the imperial pint, and milk in returnable bottles can be sold by the imperial pint. Many people measure their height in feet and inches and their weight in stone and pounds, to give just

5880-407: The base units is to make the entire system derivable from physical constants , which required the removal of the prototype kilogram as it is the last artefact the unit definitions depend on. Scientific metrology plays an important role in this redefinition of the units as precise measurements of the physical constants is required to have accurate definitions of the base units. To redefine the value of

5978-470: The classical definition, which is standard throughout the physical sciences, measurement is the determination or estimation of ratios of quantities. Quantity and measurement are mutually defined: quantitative attributes are those possible to measure, at least in principle. The classical concept of quantity can be traced back to John Wallis and Isaac Newton , and was foreshadowed in Euclid's Elements . In

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6076-472: The costs of discrepancies and measurement duplication. The OIML publishes a number of international reports in four categories: Although the OIML has no legal authority to impose its recommendations and guidelines on its member countries, it provides a standardised legal framework for those countries to assist the development of appropriate, harmonised legislation for certification and calibration. OIML provides

6174-418: The creation of the decimal-based metric system in 1795, establishing standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875; to ensure international conformity, the International Bureau of Weights and Measures ( French : Bureau International des Poids et Mesures , or BIPM) was formed by the Metre Convention . Although the BIPM's original mission

6272-460: The development of new measurement methods, the realisation of measurement standards, and the transfer of traceability from these standards to users in a society. This type of metrology is considered the top level of metrology which strives for the highest degree of accuracy. BIPM maintains a database of the metrological calibration and measurement capabilities of institutes around the world. These institutes, whose activities are peer-reviewed, provide

6370-475: The easiest-observed societal impacts. To facilitate fair trade, there must be an agreed-upon system of measurement. The ability to measure alone is insufficient; standardisation is crucial for measurements to be meaningful. The first record of a permanent standard was in 2900 BC, when the royal Egyptian cubit was carved from black granite . The cubit was decreed to be the length of the Pharaoh's forearm plus

6468-579: The exception of a few fundamental quantum constants, units of measurement are derived from historical agreements. Nothing inherent in nature dictates that an inch has to be a certain length, nor that a mile is a better measure of distance than a kilometre . Over the course of human history, however, first for convenience and then for necessity, standards of measurement evolved so that communities would have certain common benchmarks. Laws regulating measurement were originally developed to prevent fraud in commerce. Units of measurement are generally defined on

6566-428: The expected value of a quantity, and then, using various methods and instruments, reduces the uncertainty in the value. In this view, unlike the positivist representational theory, all measurements are uncertain, so instead of assigning one value, a range of values is assigned to a measurement. This also implies that there is not a clear or neat distinction between estimation and measurement. In quantum mechanics ,

6664-403: The flow of goods and services between trading partners. A common measurement system and quality standards benefit consumer and producer; production at a common standard reduces cost and consumer risk, ensuring that the product meets consumer needs. Transaction costs are reduced through an increased economy of scale . Several studies have indicated that increased standardisation in measurement has

6762-407: The fundamental reference points for metrological traceability. In the area of measurement, BIPM has identified nine metrology areas, which are acoustics, electricity and magnetism, length, mass and related quantities, photometry and radiometry, ionizing radiation, time and frequency, thermometry, and chemistry. As of May 2019 no physical objects define the base units. The motivation in the change of

6860-411: The hierarchy of metrology: primary, secondary, and working standards. Primary standards (the highest quality) do not reference any other standards. Secondary standards are calibrated with reference to a primary standard. Working standards, used to calibrate (or check) measuring instruments or other material measures, are calibrated with respect to secondary standards. The hierarchy preserves the quality of

6958-524: The higher standards. An example of a standard would be gauge blocks for length. A gauge block is a block of metal or ceramic with two opposing faces ground precisely flat and parallel, a precise distance apart. The length of the path of light in vacuum during a time interval of 1/299,792,458 of a second is embodied in an artefact standard such as a gauge block; this gauge block is then a primary standard which can be used to calibrate secondary standards through mechanical comparators. Metrological traceability

7056-429: The human body is challenging, with poor repeatability and reproducibility , and advances in metrology help develop new techniques to improve health care and reduce costs. Environmental policy is based on research data, and accurate measurements are important for assessing climate change and environmental regulation. Aside from regulation, metrology is essential in supporting innovation, the ability to measure provides

7154-419: The individual states. The International System of Units (SI) defines seven base units: length , mass , time , electric current , thermodynamic temperature , amount of substance , and luminous intensity . By convention, each of these units are considered to be mutually independent and can be constructed directly from their defining constants. All other SI units are constructed as products of powers of

7252-487: The instrument history, manufacturer's specifications, or published information. Several international organizations maintain and standardise metrology. The Metre Convention created three main international organizations to facilitate standardisation of weights and measures. The first, the General Conference on Weights and Measures (CGPM), provided a forum for representatives of member states. The second,

7350-534: The measurement unit can only ever change through increased accuracy in determining the value of the constant it is tied to. The first proposal to tie an SI base unit to an experimental standard independent of fiat was by Charles Sanders Peirce (1839–1914), who proposed to define the metre in terms of the wavelength of a spectral line . This directly influenced the Michelson–Morley experiment ; Michelson and Morley cite Peirce, and improve on his method. With

7448-418: The measurement value and uncertainty of the device that is being calibrated (the comparator) and create a traceability link to the measurement standard. The four primary reasons for calibrations are to provide traceability, to ensure that the instrument (or standard) is consistent with other measurements, to determine accuracy, and to establish reliability. Traceability works as a pyramid, at the top level there

7546-609: The measurement. Recognition of the metrological competence in industry can be achieved through mutual recognition agreements, accreditation, or peer review. Industrial metrology is important to a country's economic and industrial development, and the condition of a country's industrial-metrology program can indicate its economic status. Legal metrology "concerns activities which result from statutory requirements and concern measurement, units of measurement , measuring instruments and methods of measurement and which are performed by competent bodies". Such statutory requirements may arise from

7644-446: The metre and for mass, the kilogram. It exists in several variations, with different choices of base units , though these do not affect its day-to-day use. Since the 1960s, the International System of Units (SI) is the internationally recognised metric system. Metric units of mass, length, and electricity are widely used around the world for both everyday and scientific purposes. The International System of Units (abbreviated as SI from

7742-550: The metric system between 1795 and 1875; to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention . This has evolved into the International System of Units (SI) as a result of a resolution at the 11th General Conference on Weights and Measures (CGPM) in 1960. Metrology is divided into three basic overlapping activities: These overlapping activities are used in varying degrees by

7840-459: The necessary criteria. Three type of representational theory All data are inexact and statistical in nature. Thus the definition of measurement is: "A set of observations that reduce uncertainty where the result is expressed as a quantity." This definition is implied in what scientists actually do when they measure something and report both the mean and statistics of the measurements. In practical terms, one begins with an initial guess as to

7938-404: The need for protection of health, public safety, the environment, enabling taxation, protection of consumers and fair trade. The International Organization for Legal Metrology ( OIML ) was established to assist in harmonising regulations across national boundaries to ensure that legal requirements do not inhibit trade. This harmonisation ensures that certification of measuring devices in one country

8036-415: The photographs on this page, a two-metre carpenter's rule can be folded down to a length of only 20 centimetres, to easily fit in a pocket, and a five-metre-long tape measure easily retracts to fit within a small housing. Time is an abstract measurement of elemental changes over a non-spatial continuum. It is denoted by numbers and/or named periods such as hours , days , weeks , months and years . It

8134-496: The quotient of two integers (as long as the denominator is non-zero). A more detailed definition goes as follows: Or more formally: The existence of irrational numbers —numbers that are not a quotient of two integers—was first discovered in geometry, in such things as the ratio of the diagonal to the side in a square. Outside of arithmetic, many branches of mathematics have borrowed the word "quotient" to describe structures built by breaking larger structures into pieces. Given

8232-408: The realisation of the unit definition is propagated down through the pyramid. The traceability chain works upwards from the bottom of the pyramid, where measurements done by industry and testing laboratories can be directly related to the unit definition at the top through the traceability chain created by calibration. Measurement uncertainty is a value associated with a measurement which expresses

8330-401: The realisation of these units of measurement in practice, and the application of chains of traceability (linking measurements to reference standards). These concepts apply in different degrees to metrology's three main fields: scientific metrology; applied, technical or industrial metrology, and legal metrology. Scientific metrology is concerned with the establishment of units of measurement,

8428-432: The representational theory, measurement is defined as "the correlation of numbers with entities that are not numbers". The most technically elaborated form of representational theory is also known as additive conjoint measurement . In this form of representational theory, numbers are assigned based on correspondences or similarities between the structure of number systems and the structure of qualitative systems. A property

8526-438: The requirements of additive conjoint measurement. One may assign a value to a person's height, but unless it can be established that there is a correlation between measurements of height and empirical relations, it is not a measurement according to additive conjoint measurement theory. Likewise, computing and assigning arbitrary values, like the "book value" of an asset in accounting, is not a measurement because it does not satisfy

8624-428: The results need to be corrected for measurement errors . The following rules generally apply for displaying the exactness of measurements: Since accurate measurement is essential in many fields, and since all measurements are necessarily approximations, a great deal of effort must be taken to make measurements as accurate as possible. For example, consider the problem of measuring the time it takes an object to fall

8722-515: The same base but different prefixes. To convert from metres to centimetres it is only necessary to multiply the number of metres by 100, since there are 100 centimetres in a metre. Inversely, to switch from centimetres to metres one multiplies the number of centimetres by 0.01 or divides the number of centimetres by 100. A ruler or rule is a tool used in, for example, geometry , technical drawing , engineering, and carpentry, to measure lengths or distances or to draw straight lines. Strictly speaking,

8820-436: The seven base units. Since the base units are the reference points for all measurements taken in SI units, if the reference value changed all prior measurements would be incorrect. Before 2019, if a piece of the international prototype of the kilogram had been snapped off, it would have still been defined as a kilogram; all previous measured values of a kilogram would be heavier. The importance of reproducible SI units has led

8918-411: The spread of possible values associated with the measurand —a quantitative expression of the doubt existing in the measurement. There are two components to the uncertainty of a measurement: the width of the uncertainty interval and the confidence level. The uncertainty interval is a range of values that the measurement value expected to fall within, while the confidence level is how likely the true value

9016-414: The suitability of measurement instruments, their calibration and quality control. Producing good measurements is important in industry as it has an impact on the value and quality of the end product, and a 10–15% impact on production costs. Although the emphasis in this area of metrology is on the measurements themselves, traceability of the measuring- device calibration is necessary to ensure confidence in

9114-562: The three basic sub-fields of metrology: In each country, a national measurement system (NMS) exists as a network of laboratories, calibration facilities and accreditation bodies which implement and maintain its metrology infrastructure. The NMS affects how measurements are made in a country and their recognition by the international community, which has a wide-ranging impact in its society (including economics, energy, environment, health, manufacturing, industry and consumer confidence). The effects of metrology on trade and economy are some of

9212-450: The varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units (SI). This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement

9310-476: The width of his hand, and replica standards were given to builders. The success of a standardised length for the building of the pyramids is indicated by the lengths of their bases differing by no more than 0.05 per cent. In China weights and measures had a semi religious meaning as it was used in the various crafts by the Artificers and in ritual utensils and is mentioned in the book of rites along with

9408-477: The word "quotient" refers to the whole. 1 2 ← dividend or numerator ← divisor or denominator } ← quotient {\displaystyle {\dfrac {1}{2}}\quad {\begin{aligned}&\leftarrow {\text{dividend or numerator}}\\&\leftarrow {\text{divisor or denominator}}\end{aligned}}{\Biggr \}}\leftarrow {\text{quotient}}} The quotient

9506-410: The world. The chain of traceability allows any measurement to be referenced to higher levels of measurements back to the original definition of the unit. Traceability is obtained directly through calibration , establishing the relationship between an indication on a standard traceable measuring instrument and the value of the comparator (or comparative measuring instrument). The process will determine

9604-509: Was to create international standards for units of measurement and relate them to national standards to ensure conformity, its scope has broadened to include electrical and photometric units and ionizing radiation measurement standards. The metric system was modernised in 1960 with the creation of the International System of Units (SI) as a result of a resolution at the 11th General Conference on Weights and Measures ( French : Conference Generale des Poids et Mesures , or CGPM). Metrology

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