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Measurement Systems

Measurement Systems    Gravimetric


SI Principles    SI Base Units
SI Derived Units    SI Prefixes

SI - Système International

The 11th CGPM (1960) adopted a first series of prefixes and symbols of prefixes to form the names and symbols of decimal multiples and sub-multiples of SI units. Over the years the list has been extended to the following: SI Prefixes

SI stands for Système International d’Unités, or the International System of Units. SI is the abbreviation used in all languages to indicate this system.

SI - Principles of the system

The SI is constructed from seven Base Units, which are defined in physical terms. By combining these units in accordance with simple geometrical and physical laws, we can arrive at the Derived Units. For practical reasons, 21 of the derived units have their own names.

In principle, the SI covers all application areas, although certain units outside SI are so useful that they are accepted for general use together with the SI. These units are referred to as additional units, of which the most common are: degree, minute and second for plane angle, litre for volume, minute, hour and day for time and tonne for mass.

Further information on the SI system can be obtained from the book Le Système International d’Unités, published by the Bureau International des Poids et Mesures, BIPM, Pavillon de Breteuil, F-92319 Sèvres, Cedex, France. Information on SI can also be obtained from standards in the ISO 31 series.

SI - Base Units

The International System (SI) of comprised of seven base units: physical units defined by an operational definition. All but one of these is independently reproducible through experiment. The kilogram is the only base unit still tied to a physical artifact.

All other physical units can be derived from these base units: these are known as the SI derived units. Derivation is by dimensional analysis. SI prefixes are used to abbreviate long positive and negative numbers.

The following are the base units from which all others are derived; they are dimensionally independent.

  1. "The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom"
    (13th CGPM, 1967, Resolution 1)
  2. "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second"
    (17th CGPM, 1983, Resolution 1)
  3. "The kilogram is the unit of mass: it is equal to the mass of the international prototype of the kilogram"
    (1st CGPM, 19989 & 3rd CGPM, 1901)
  4. "The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0,012 kilogram of carbon 12."
    (14th CGPM 1971)
  5. "The kelvin, unit of thermodynamic temperature, is the fraction 1/273,16 of the thermodynamic temperature of the triple point of water"
    (13th CGPM, 1967, Resolution 4)
  6. "The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of (1/683) watt per steradian"
    (16th CGPM, 1979, Resolution 3)
  7. "The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between theses conductors a force equal to 2 x 10-7 newton per metre of length"
    (9th CGPM 1948)

SI - Derived Units

The SI is constructed from seven Base Units, which are defined in physical terms. By combining these units in accordance with simple geometrical and physical laws, we can arrive at the Derived Units. For practical reasons, the derived units have their own names. There are 20 derived units as well as two special derived units which are dimensionless. These dimensionless units are ratios formed by dividing two SI units.

Quantity SI dimensionless unit
Name Definition
plane angle radian rad m·m-1 = 1
The unit of angle is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle. There are radians in a circle.
solid angle steradian  sr m2·m-2 = 1
The unit of solid angle is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r2. There are steradians on a sphere. (m2·m-2 = 1)

Quantity SI derived unit

Name

in terms of other units... Expression in terms of SI base units
frequency hertz Hz   s-1
force newton N   m·kg·s-2
pressure, stress pascal Pa N/m2 m-1·kg·s-2
energy, work, quantity of heat joule J N·m m2·kg·s-2
power, radiant flux watt W J/s m2·kg·s-3
electric charge, quantity of electricity coulomb C   s·A
electric potential difference, electromotive force volt V W/A m2·kg·s-3·A-1
capacitance farad F C/V m-2·kg-1·s4·A2
electric resistance ohm W V/A m2·kg·s-3·A-2
electric conductance siemens S A/V m-2·kg-1·s3·A2
magnetic flux weber Wb V·s m2· kg·s-2·A-1
magnetic flux density tesla T Wb/m2 kg·s-2·A-1
inductance henry H Wb/A m2· kg·s-2·A-2
Celsius temperature degree Celsius °C °C = K-273.15 K
luminous flux lumen lm cd·sr  m2·m-2·cd = cd
illuminance lux lx lm/m2 m2·m-4·cd = m-2·cd
radioactivity (decay/time) becquerel Bq   s-1
absorbed dose (kerma), (ionizing radiation) gray Gy J/kg m2·s-2
dose equivalent, (ionizing radiation) sievert Sv J/kg m2·s-2
Catalytic Activity katal kat mol/s s-1·mol

SI - Prefixes

A prefix combined with a unit indicates that the unit is multiplied by a particular power of ten. The new unit is referred to as a multiple unit. There are 20 standardised prefixes. The choice of prefix depends on purely practical considerations: in practice, it should be chosen such that the resulting numeral lies between 0.1 and 1000. Prefixes that indicate multiplication by 1000 or 1/1000 should preferably be chosen.

The 11th CGPM (1960) adopted a first series of prefixes and symbols of prefixes to form the names and symbols of decimal multiples and sub-multiples of SI units. Over the years the list has been extended to the following:

Factor Prefix Symbol Unit
1024yottaY1 000 000 000 000 000 000 000 000
1021zettaZ1 000 000 000 000 000 000 000
1018exaE 1 000 000 000 000 000 000
1015petaP 1 000 000 000 000 000
1012teraT 1 000 000 000 000
109gigaG 1 000 000 000
106megaM 1 000 000
103kilok 1 000
102hectoh 100
101decada 10
10-1decid 0.1
10-2centic 0.01
10-3millim 0.001
10-6microµ0.000 001
10-9nanon 0.000 000 001
10-12picop 0.000 000 000 001
10-15femtof 0.000 000 000 000 001
10-18attoa 0.000 000 000 000 000 001
10-21zeptoz 0.000 000 000 000 000 000 001
10-24yoctoy 0.000 000 000 000 000 000 000 001

1018 one quintillion 10-18 one quintillionth
1015 one quadrillion 10-15 one quadrillionth
1012 one trillion 10-12 one trillionth
109 one billion 10-9 one billionth
106 one million 10-6 one millionth
103 one thousand 10-3 one thousandth
102 one hundred 10-2 one hundredth
101 ten 10-1 one tenth
100 one 10-0 undefined

Last modified: 29 November 2007 00:36:37