International System of Units
The International System of Units or SI ( Système international d' of French Units) units is the most widely used system of units of physical quantities. It is a coherent metric system of units.
- 7.1 Related spelling of quantities, numerical values and units
- 7.2 Name and symbols of sizes
- 7.3 spelling of the unit mark 7.3.1 decimal separator and thousands separator
- 7.3.2 Uncertainty in numerical values
Introduction
The SI is a metric, decimal and coherent system of units. By SI physical units are defined on selected sizes. The selection is made - in accordance with current scientific theories - for practical considerations. The SI is based on seven ( defined by convention ) base units with corresponding base sizes.
For international regulations concerning the SI is the international office of weights and measures ( BIPM) in charge. As a reference set of rules by the BIPM at periodic intervals (usually every few years) applies newly published brochure Le Système international d' unités - German referred to simply as " the SI brochure". This article refers to the 2006 released 8th edition of the SI brochure.
Usually the national metrology institutes are responsible for the national implementation of the SI.
These are, for example,
- In Germany, the Physikalisch-Technische Bundesanstalt ( PTB) ( in the GDR it was the Office of Standards, Metrology and Inspection of goods ( ASMW ) )
- In Switzerland, the Swiss Federal Institute of Metrology (METAS )
- In Austria, the Federal Office of Metrology and Surveying (BEV )
- In the UK, the National Physical Laboratory ( NPL) and
- In the U.S., the National Institute of Standards and Technology ( NIST).
These national recommendations received legal significance (that is essentially an application requirement in some activity) only by laws or jurisdiction of individual states.
In the EU, the use of units, among others, by the EC Directive 80/181/EEC has largely been unified. In the European Union ( EU), Switzerland and most other countries, the use of the SI in the official or commercial transactions is required by law. Directive 2009/3/EC of the use of additional information on the European Union was allowed unlimited ( by previous guidelines, this was originally only until December 31, 2009 possible). This is mainly due so as not to hinder exports of goods to third countries. In many countries, national laws allow certain exceptions to the SI rules.
From the U.S., Myanmar and Liberia, the SI system was never officially introduced. In the U.S., metric units are for a parliamentary decision in 1866, a government decree in 1894 recognized units. In the 1970s, considerable efforts have been made to introduce the SI system, but it failed because of the lack of will of the user or person concerned. In many areas such as science, medicine and industry, the SI system is used exclusively or in parallel. Otherwise, the Anglo-American system of measurement in the variant of " customary units" in the United States ( based on a historical form of the British system of measurement ) are common.
Metre Convention, the BIPM and CGPM
Milestone for the international enforcement of the metric system was the signing of the Metre Convention in 1875 by 17 States. Here also, the International Bureau of Weights and Measures (BIPM ) and its General Conference on Weights and Measures ( CGPM ) was established. These two institutions are responsible today for the international standardization of the SI.
History
Dissemination
The SI is now widespread throughout the world. In most industrialized countries, its use for official and commercial traffic is required by law. In Germany this is done by the Units and Time Act and the associated implementing regulations. Laws that governed the introduction of the SI occurred in 1970 in the Federal Republic of Germany, in 1973 in Austria and in Switzerland in 1978 is in force; 1978 all transitional arrangements were completed concerning non-SI units. In Germany, most textbooks have been converted to SI units. An exception to the textbooks on electrodynamics and particle physics.
In some countries, traditional notation are in addition to the SI continues to be used:
- In the U.S., SI units for distances, areas, velocities and temperature have prevailed only in the scientific and technical context.
- In Britain, the traditional units are pushed back in many areas, they still consider themselves to be distance and temperature data.
In aviation, we will continue to use non- SI -compliant units for altitude ( ft = feet ), distances ( nautical mile = 1852 m) and speeds ( 1KT = 1 knot = 1 nautical mile per hour).
SI units
In SI there are seven base units. All other physical units are derived from these basic units. All physical units form the coherent SI units, unless they are used together with SI prefixes (like kilo or milli). An exception is the kilogram, which is provided as the basic unit already with the SI prefix kilo. By use of SI prefixes coherent SI units SI units are non-coherent. The total of all of these units, ie both the coherent and non-coherent, the SI units is the set of " SI " units.
- The length unit meter (m ) is an SI base unit, a coherent SI unit and a SI unit.
- The mass unit kilogram ( kg ) is an SI base unit, a coherent SI unit and a SI unit.
- The force unit Newton ( N) is a derived SI unit and a coherent SI unit.
- The power unit kilo Newton ( kN) is a derived SI unit, but no coherent SI unit.
A SI base unit is always the coherent unit of the corresponding basic size. In addition, they can also serve as a cohesive unit derived quantities.
- The meter (m) is the basic unit of the base size length. In addition, it also serves as a coherent derived unit for rainfall, which is expressed as volume per area in m³ / m² = m.
- The ampere is the SI base unit of electric current and at the same time coherent derived SI unit of magnetic flux.
The term " SI unit " is often used in the sense of " legal entity " or " recommended unit ". However, there are also legal entities that are not SI units. Such types of misuse are found, however, even with standardization organizations. Thus we read in the national annex to the German standard DIN ISO 8601:2006-09: " The spelling of times with the physical SI units h, min, s according to DIN 1301-1 should be avoided." The use of such non - SI units with SI units is indeed sanctioned - see below - but they are not thereby to SI units.
SI base units
The base units of the SI and the corresponding basic variables of the underlying system size ISQ be arbitrarily determined on practical considerations by the CGPM. A SI base size can by definition not be expressed by different base sizes. Analogously, an SI base unit can not be expressed as a product of powers of other base units.
The definitions of the base units are not final, but will be continued in constant work with the progressive state of the art measurement methods including after revised basic considerations. In international sizes and unit system, the seven base quantities by the base units meter (m), kilogram ( kg), second ( s ), ampere (A), kelvin ( K), mole ( mol), and candela ( cd) expressed and in SI in this order. Each basic variable is assigned a dimension with the same name. For example, is called the dimension of the base size length also length. The symbol size is denoted by a italicized letter " l"; that the dimension with an upright, upper-case letter " L". The practical realization of a dimension is carried out by a corresponding coherent unit - in the case of length by the meter.
It can be seen that only the three basic units of kilograms, and second Kelvin are defined independently of the other base units, while the definitions of the remaining four base units have dependencies from other base units:
- Meters of second
- Mole of kilogram
- Ampere and candela of meters, kilograms and seconds
Furthermore, it is striking that only the unit kilogram is defined in terms of a prototype. All other units are determined by immutable constants of nature, but this was not always the case. So it was until 1960, for example, a standard meter as a prototype for the meter unit. Since the weight of the Urkilogramms could change but theoretically (and probably does) works by the fact to define the unit of kilograms uniquely (see also definition of the kilogram ).
Coherent SI units
All physical quantities other than the above seven base quantities of the ISQ are derived quantities. Similarly, all units except the seven base units of the SI derived units are.
The SI unit of any size Q ( is short for quantity. ) Can always be expressed as the product of a numerical factor and the product of magnitude ( power product ) of the base units:
" [Q ] " symbolically represents the expression " the unity of the quantity Q " represents, in agreement with the rules according to the published by the Joint Committee for Guides in Metrology, VIM (International Vocabulary of Metrology - Basic and General Concepts and Associated Terms ).
The numerical factor 10n ( with integer n) represents the SI prefix such as kilo or milli. If the numerical factor equal to one (ie n = 0), there is a coherent SI unit. Every physical quantity has only a single coherent SI unit and a corresponding dimension. A coherent SI unit is using an SI prefix to a non-coherent SI unit. The coherent form above unit equation can be represented as a corresponding dimension equation:
The base of each power is in this representation, the dimension of the base size. The exponent is called the dimension exponent of this base size or the corresponding base unit. Each dimension exponent α, β, γ, δ, ε, ζ, and η is either zero or a positive or negative integer generally. The magnitude of the exponents is significantly smaller than 10 in the control
Examples of coherent SI units ( n = 0)
- M ( α = 1, all other dimension exponent equal to 0 ) as the basic unit of length
- M2 ( α = 2, all other dimension exponent equal to 0 ), the unit of area
- M · s- 1 = m / s ( α = 1 and γ = -1, and all other dimension exponent equal to 0 ), the unit of speed
- M · kg · s-2 = m · kg/s2 = N ( α = 1, β = 1 and γ = -2, all other dimension exponent equal to 0 ) as the unit of force
Examples of non- coherent SI units ( n ≠ 0)
- Mm ( n = -3 ≠ 0)
An advantage of the exclusive use of coherent SI units in equations is that no conversion factors are required between units.
Derived SI units with special names
22 coherent SI derived units have been assigned their own names and symbols ( symbols) that can be re- combined with all base and derived units themselves. Thus, for example, is the SI unit of force, the newton ( = kg · m/s2) to express the unit of energy, the joule as Newton times meter (N · m). The following table lists these 22 units in the same order as Table 3 of the SI brochure ( 8th edition ).
Non- SI units
In addition to the SI units, there are (especially in electrodynamics, computer science, marketing services) some other common units that are not part of the SI, in particular the so-called Gaussian or cgs system.
Notation of quantities, numerical values and units
The ISO 1000:1992 has been withdrawn in 2009 after the ISO / IEC 80000-1. was published. National and International standards such as ISO 1000 or appropriate EEC directives have taken over the SI. In Germany specified within the units with the law on units in measuring technology (1969 ) were ( which was enlarged in 2008 by incorporating the terms of the previous time law to the law relating to units of measurement and the determination of time ( EinhZeitG )) for the official and commercial traffic prescribed. The current executive order from 1985 calls in a system, the allowable designations and refers to the rest of " the definitions and relationships in Chapter I of the Annex to Directive 80/181/EG of 20 December 1979 ( OJ L 39, 15.2. 1980, p 40 ) are listed in effect at the time. " According to § 3 of Regulation ", the additional use of other than the legal units is only allowed if the line is emphasized in the legal unit. ", the previous regulation had quite a few non- SI units with no additives allowed, for example mmHg ( millimeters of mercury ) for blood pressure. In Switzerland, the designation mmHg for the pressure of other body fluids is allowed. The SI of rules called for its part, non-SI units whose use is accepted along with the SI. The SI brochure regulates not only the unit name, but also gives formatting rules apply to writing the unit symbols and numerical values.
Related spelling of quantities, numerical values and units
According to ISO size icons ( symbols ) are to be written in italics, unit symbol in an upright font. Size information should always be made with numerical value and unit; no multiplication sign between them:
It says A ( advertised or as one character ) as a symbol for the size, {A } for the numerical value of A and [A ] for the unit of A.
From this coherent notation is waived if many similar size information must be provided in tables or axis labels. It is recommended for the notation A / [A ] = { A}, eg T / K = 300, 400, 500 for T = 300 K, 400 K, 500 K. Motivation: If we imagine instead of size T the product of numerical value and unit, then the unit truncates away. To avoid confusion, if the unit is a break even, it is recommended individually to set negative exponent to unity sign of the denominator, for a thermal resistance R in Kelvin per watt so R / K W -1. Non-standard, but more usually the spellings R in K / W, R (K / W) and R [ K / W].
Name and symbols of sizes
Size icons ( symbols ) are to be written in italics. The characters can be chosen freely - generally used symbols such as l, m, or t only make recommendations dar. Even DIN standards include recommendations for symbols. The choice of name and symbol of a physical quantity recommends the SI brochure without association to a particular unit. Thus, terms are to be avoided as output per liter. The Celsius temperature does not obey this recommendation, however. Further, although not as important examples of non - compliance with this recommendation are the hour angle, the number of degree days and the heating degree day.
Spelling of the unit mark
The unit symbol of non-assembled units are internationally uniform. Regardless of the format of the surrounding text they are writing in an upright font. They are written in lowercase letters, unless they were named after a person - then the first letter is capitalized. Example: " 1 s " means a second, while " 1 S" represents by Werner von Siemens Siemens named. An exception to this rule is the non-SI unit liter: although it is not named after a person, can for their unit symbol next to the lowercase l and the uppercase L are used. The latter is mainly in the Anglo-American common, to avoid confusion with the numeral "one."
An SI prefix (such as kilo or milli) can be provided for a decimal multiple or part directly to the symbol of a coherent unit to represent units in different orders of magnitude clearer. An exception is the kilogram ( kg), which may be used starting only from gram (g) with SI prefixes. For example, it has to 10-6 kg "mg" hot and not " μkg ".
Unit characters follow after a space the numerical value, even in percentage and temperature in degrees Celsius. For better legibility and avoid line breaks a narrow space should be used. Only the unit symbols °, ' and "for the non-SI units of angle degrees, minutes and seconds are set directly after the number without space.
Notes on certain matters are not to be attached to unit symbols (as subscript ); they belong, however, to the symbols of the physical quantity used or explanatory text. Wrong is Veff as a " unit " of rms values of the electrical voltage in volts VDC for specifying an electrical DC voltage in volts, or% (V / V ) for " volume percent ".
Dimension symbols are written as upright uppercase sans serif font.
Language-specific notation:
One unit has a prescribed unit name and unit symbols. Depending on the language (ly dt Lj, engl. ) Are different spellings for both unit names ( dt seconds, Eng. Secondhand, French seconde ) and for unit symbols provided.
Decimal separator and thousands separator
In the SI brochure 5.3.4 decimal and thousand separators are treated in section:
- As the decimal either ( depending on the language ), a comma or a point on the line is allowed - otherwise must not be used within the number comma or period.
Uncertainty in numerical values
If the numerical value of a quantity can only be estimated, so the uncertainty shall be stated. The guidelines issued by the Joint Committee for Guides in Metrology Guide to the Expression of Uncertainty in Measurement (GUM ) are enforced.
The following example shows using the 2010 CODATA recommended by the value of the Avogadro constant NA is the compact notation for specifying the standard uncertainty (from 2.7 × 1016 mol -1):
This expression is equivalent to the long spelling of the form:
Future developments
As seen from the above currently valid Definitions of SI base units seen an exact numerical value has been set for the previous two fundamental physical constants ( constants of nature ). This was useful because these natural constants were determined more accurately than the basic units involved (the largest contribution to the uncertainty of the numerical value derived from the units). As a result of these measurements are fundamental constants of the representation defined by it base unit:
- The definition of the ampere in 1948 based on the definition of the numerical value of the magnetic constant μ0 = 4 π · 10-7 H · m -1 = 4π · 10-7 m · kg · s-2 · A-2. The base unit ampere - and all other electrical units - is therefore based on a natural constant to the base units meter, kilogram, and second.
- The 1983 made redefinition of the meter is based on the speed of light in vacuum: The definition of c = 299 792 458 m · s- 1 refers to the meter to the second.
In the future, further redefinitions of SI base units are expected, associated with an exact determination of some constants of nature. Possible redefinitions of SI base units are discussed on the all four -yearly General Conference on Weights and Measures.
The following are the proposed with status 2011 redefinitions of SI base units are combined.
Second
The proposed redefinition corresponding to the previous definition, with the difference that the measurement conditions are aggravated.
Meter
The proposed redefinition corresponds to the previous definition.
Kilogram
The definition of the kilogram is changing significantly. Meanwhile, new definition is no longer based on a prototype, but on the defined exactly as Planck 's constant with the unit s-1 · m2 · kg, which corresponds to the unit J · s.
One consequence would be that the kilogram in contrast to the previous definition of the definition of the second and the meter is dependent.
Ampere
The definition of the ampere is changed in the proposal that it is measured technically easier to implement than the previous definition. The new definition is based on the precisely defined elementary charge e
One consequence would be that the amp is no longer based on the definition of the kilogram and the meter. In addition, by exact definition of the elementary charge would be the previously precisely defined magnetic field constant, the electric field constant, and from this and the wave impedance of the vacuum no longer precisely defined.
Kelvin
The proposed redefinition of the kelvin is based on the exact determination of the Boltzmann constant k
One consequence would be that the definition of the kelvin on the definition of second, meters and kilograms based.
Mole
The definition of the mole is associated with the determination of the Avogadro constant NA. Thus, there would be no dependence on the kilograms more.
Candela
The proposed redefinition corresponds to an amendment to the wording of the previous definition.