A unit of measurement is a definite magnitude of a quantity, defined
and adopted by convention or by law, that is used as a standard for
measurement of the same kind of quantity.[1] Any other quantity of
that kind can be expressed as a multiple of the unit of measurement.
For example, a 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".
Contents 1 History 2 Systems of units 2.1 Traditional systems 2.2 Metric systems 2.3 Natural systems 2.4 Legal control of weights and measures 3 Base and derived units 4 Calculations with units of measurement 4.1 Units as dimensions 4.2 Expressing a physical value in terms of another unit 5 Real-world implications 6 See also 7 Notes 8 External links History[edit]
Main article: History of measurement
A unit of measurement is a standardised quantity of a physical
property, used as a factor to express occurring quantities of that
property.
An example of metrication in 1860 when Tuscany became part of modern Italy (ex. one "libbra" = 339.54 grams) Both the imperial units and
Z = n × [ Z ] = n [ Z ] . displaystyle Z=ntimes [Z]=n[Z]. For example, let Z displaystyle Z be "2 candlesticks", then Z = 2 [ Z ] = 2 displaystyle Z=2[Z]=2 candlestick. 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. 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. Let Z 1 displaystyle Z_ 1 be "2 candlesticks" and Z 2 displaystyle Z_ 2 "3 cabdrivers", then "2 candlesticks" times "3 cabdrivers" = 6 [ Z 1 ] [ Z 2 ] = 6 displaystyle =6[Z_ 1 ][Z_ 2 ]=6 candlestick × displaystyle times cabdriver. 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.
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 or divided, 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. m2/s2). Put simply, units obey the laws of indices. (See Exponentiation.) Some units have special names, however these should be treated like their equivalents. For example, one newton (N) is equivalent to 1 kg⋅m/s2. 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/s2 (kilograms per second squared). Whether these designations are equivalent is disputed amongst metrologists.[5] Expressing a physical value in terms of another unit[edit]
Z = n i × [ Z ] i displaystyle Z=n_ i times [Z]_ i just replace the original unit [ Z ] i displaystyle [Z]_ i with its meaning in terms of the desired unit [ Z ] j displaystyle [Z]_ j , e.g. if [ Z ] i = c i j × [ Z ] j displaystyle [Z]_ i =c_ ij times [Z]_ j , then: Z = n i × ( c i j × [ Z ] j ) = ( n i × c i j ) × [ Z ] j displaystyle Z=n_ i times (c_ ij times [Z]_ j )=(n_ i times c_ ij )times [Z]_ j Now n i displaystyle n_ i and c i j displaystyle c_ ij are both numerical values, so just calculate their product. Or, which is just mathematically the same thing, multiply Z by unity, the product is still Z: Z = n i × [ Z ] i × ( c i j × [ Z ] j / [ Z ] i ) displaystyle Z=n_ i times [Z]_ i times (c_ ij times [Z]_ j /[Z]_ i ) For example, you have an expression for a physical value Z involving the unit feet per second ( [ Z ] i displaystyle [Z]_ i ) and you want it in terms of the unit miles per hour ( [ Z ] j displaystyle [Z]_ j ): Find facts relating the original unit to the desired unit: 1 mile = 5280 feet and 1 hour = 3600 seconds 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: 1 = 1 m i 5280 f t a n d 1 = 3600 s 1 h displaystyle 1= frac 1,mathrm mi 5280,mathrm ft quad mathrm and quad 1= frac 3600,mathrm s 1,mathrm h 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. 52.8 f t s = 52.8 f t s 1 m i 5280 f t 3600 s 1 h = 52.8 × 3600 5280 m i / h = 36 m i / h displaystyle 52.8, frac mathrm ft mathrm s =52.8, frac mathrm ft mathrm s frac 1,mathrm mi 5280,mathrm ft frac 3600,mathrm s 1,mathrm h = frac 52.8times 3600 5280 ,mathrm mi/h =36,mathrm mi/h 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: 9 L 100 k m = 9 L 100 k m 1000000 μ L 1 L 1 k m 1000 m = 9 × 1000000 100 × 1000 μ L / m = 90 μ L / m displaystyle mathrm frac 9, rm L 100, rm km =mathrm frac 9, rm L 100, rm km mathrm frac 1000000, rm mu L 1, rm L mathrm frac 1, rm km 1000, rm m = frac 9times 1000000 100times 1000 ,mathrm mu L/m =90,mathrm mu L/m Real-world implications[edit]
List of humorous units of measurement
List of unusual units of measurement
GNU Units
Unified Code for Units of Measure
v t e Systems of measurement Current General
Specific Apothecaries' Avoirdupois Troy Astronomical Electrical Temperature Natural atomic geometrised Gaussian Lorentz–Heaviside Planck quantum chromodynamical Stoney Background Metric Overview Introduction Outline History Metrication UK/US Overview Comparison Foot–pound–second (FPS) Historic Metric metre–kilogram–second (MKS) metre–tonne–second (MTS) centimetre–gram–second (CGS) gravitational quadrant–eleventh-gram–second (QES) (hebdometre–undecimogramme–second (HUS)) Europe Byzantine Cornish Cypriot Czech Danish Dutch English Estonian Finnish French (Trad. • Mesures usuelles) German Greek Hungary Icelandic Irish Scottish Italian Latvia Luxembourgian Maltese Norwegian Ottoman Polish Portuguese Romanian Russian Serbian Slovak Spanish Swedish Switzerland Welsh Winchester measure Asia Afghan Cambodian Chinese Hindu Hong Kong India Indonesian Japanese Korean Mongolian Omani Philippine Pegu Singaporean Sri Lankan Syrian Taiwanese Tatar Thai Vietnamese Africa Algerian Ethiopian Egyptian Eritrean Guinean Libyan Malagasy Mauritian Moroccan Seychellois Somalian South African Tunisian Tanzanian North America Costa Rican Cuban Haitian Honduran Mexico Nicaraguan Puerto Rican South America Argentine Brazilian Chilean Colombian Paraguayan Peruvian Uruguayan Venezuelan Ancient Arabic Biblical and Talmudic Egyptian Greek Hindu Indian Mesopotamian Persian Roman List articles Humorous (FFF system) Obsolete Unusual Other N-body Modulor Notes[edit] ^ "measurement unit", in International Vocabulary of Metrology
– Basic and General Concepts and Associated Terms (VIM) (PDF) (3rd
ed.), Joint Committee for Guides in Metrology, 2008,
pp. 6–7 .
^ Yunus A. Çengel & Michael A. Boles (2002). Thermodynamics: An
External links[edit] Rowlett, Russ (2005) A Dictionary of Units of
Historical "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. Legal Ireland –
Metric information and associations BIPM (official site)
UK Metric Association
US Metric Association
The
Imperial measure information British Weights and Me |