Si Derived Units

8/22/2019 Si Derived Units

1/6

SI DERIVED UNITS

The International System of Units (SI) specifies a set of seven base units from which all otherunits of

measurement are formed, by products of the powers of base units. These other units are called SI derived units; for

example, the SI derived unit of area is square metre (m2), and of density is kilograms per cubic metre (kg/m

3). The

number of derived units is unlimited.

The names of SI units are always written in lowercase. The symbols of units named after persons, however, are

always written with an uppercase initial letter (e.g. the symbol of hertz is Hz; but metre is m).

Named units derived from SI base units

Name Symbol Quantity EquivalentsSI base unitEquivalents

becquerel Bq radioactivity (decays per unit time) 1/s s1

coulomb C electric charge orquantity of electricity sA sA

degree Celsius C temperature relative to 273.15 K K - 273.15 K - 273.15

farad F electric capacitance C/V kg1

m2

s4A

2

gray Gy absorbed dose (ofionizing radiation) J/kg m2s2

henry H inductanceVs/AWb/A

kgm2s

2A

2

hertz Hz frequency 1/s s1

joule J energy, work, heatNmCVWs

kgm2s

2

katal kat catalytic activity mol/s s1

mol

lumen lm luminous flux cdsr cd

lux lx illuminance lm/m m2cd

newton N force, weight kgm/s2 kgms2

ohm electric resistance, impedance, reactance V/A kgm2s

3A

2

pascal Pa pressure, stress N/m2 kgm

1s

2

radian rad angle m/m dimensionless

siemens S electrical conductance1/

A/Vkg

1m

2s

3A

2

sievert Sv equivalent dose (ofionizing radiation) J/kg m2s

2

steradian sr solid angle m2/m

2dimensionless

tesla T magnetic field strength, magnetic flux densityVs/m

2

Wb/m2N/(Am)

kgs2

A1

volt V voltage, electrical potential difference, electromotive forceW/AJ/C

kgm2s

3A

1

watt W power, radiant fluxJ/sVA

kgm2s

3

weber Wb magnetic flux J/A kgm2s

2A

1

Examples of derived quantities and units

Some SI derived units

Name Symbol QuantityExpression in terms

of SI base units

square metre m2 area m2

cubic metre m3 volume m3

metre per second m/s speed, velocity ms1

cubic metre per second m3/s volumetric flow m

3s

1
https://en.wikipedia.org/wiki/International_System_of_Unitshttps://en.wikipedia.org/wiki/SI_base_unithttps://en.wikipedia.org/wiki/Units_of_measurementhttps://en.wikipedia.org/wiki/Units_of_measurementhttps://en.wikipedia.org/wiki/SIhttps://en.wikipedia.org/wiki/Symbolhttps://en.wikipedia.org/wiki/Physical_quantityhttps://en.wikipedia.org/wiki/SI_base_unithttps://en.wikipedia.org/wiki/Becquerelhttps://en.wikipedia.org/wiki/Radioactivityhttps://en.wikipedia.org/wiki/Coulombhttps://en.wikipedia.org/wiki/Electric_chargehttps://en.wikipedia.org/wiki/Quantity_of_electricityhttps://en.wikipedia.org/wiki/Celsiushttps://en.wikipedia.org/wiki/Temperaturehttps://en.wikipedia.org/wiki/Faradhttps://en.wikipedia.org/wiki/Electric_capacitancehttps://en.wikipedia.org/wiki/Gray_(unit)https://en.wikipedia.org/wiki/Absorbed_dosehttps://en.wikipedia.org/wiki/Ionizing_radiationhttps://en.wikipedia.org/wiki/Henry_(unit)https://en.wikipedia.org/wiki/Inductancehttps://en.wikipedia.org/wiki/Hertzhttps://en.wikipedia.org/wiki/Hertzhttps://en.wikipedia.org/wiki/Frequencyhttps://en.wikipedia.org/wiki/Joulehttps://en.wikipedia.org/wiki/Energyhttps://en.wikipedia.org/wiki/Mechanical_workhttps://en.wikipedia.org/wiki/Heathttps://en.wikipedia.org/wiki/Katalhttps://en.wikipedia.org/wiki/Catalytic_activityhttps://en.wikipedia.org/wiki/Lumen_(unit)https://en.wikipedia.org/wiki/Luminous_fluxhttps://en.wikipedia.org/wiki/Luxhttps://en.wikipedia.org/wiki/Illuminancehttps://en.wikipedia.org/wiki/Newton_(unit)https://en.wikipedia.org/wiki/Forcehttps://en.wikipedia.org/wiki/Weighthttps://en.wikipedia.org/wiki/Ohm_(unit)https://en.wikipedia.org/wiki/Electric_resistancehttps://en.wikipedia.org/wiki/Electrical_impedancehttps://en.wikipedia.org/wiki/Reactance_(electronics)https://en.wikipedia.org/wiki/Pascal_(unit)https://en.wikipedia.org/wiki/Pressurehttps://en.wikipedia.org/wiki/Stress_(physics)https://en.wikipedia.org/wiki/Radianhttps://en.wikipedia.org/wiki/Anglehttps://en.wikipedia.org/wiki/Siemens_(unit)https://en.wikipedia.org/wiki/Electrical_conductancehttps://en.wikipedia.org/wiki/Sieverthttps://en.wikipedia.org/wiki/Equivalent_dosehttps://en.wikipedia.org/wiki/Ionizing_radiationhttps://en.wikipedia.org/wiki/Steradianhttps://en.wikipedia.org/wiki/Solid_anglehttps://en.wikipedia.org/wiki/Tesla_(unit)https://en.wikipedia.org/wiki/Magnetic_fieldhttps://en.wikipedia.org/wiki/Magnetic_flux_densityhttps://en.wikipedia.org/wiki/Volthttps://en.wikipedia.org/wiki/Voltagehttps://en.wikipedia.org/wiki/Electrical_potential_differencehttps://en.wikipedia.org/wiki/Electromotive_forcehttps://en.wikipedia.org/wiki/Watthttps://en.wikipedia.org/wiki/Power_(physics)https://en.wikipedia.org/wiki/Radiant_fluxhttps://en.wikipedia.org/wiki/Weber_(Wb)https://en.wikipedia.org/wiki/Magnetic_fluxhttps://en.wikipedia.org/wiki/Square_metrehttps://en.wikipedia.org/wiki/Square_metrehttps://en.wikipedia.org/wiki/Areahttps://en.wikipedia.org/wiki/Cubic_metrehttps://en.wikipedia.org/wiki/Volumehttps://en.wikipedia.org/wiki/Metre_per_secondhttps://en.wikipedia.org/wiki/Speedhttps://en.wikipedia.org/wiki/Velocityhttps://en.wikipedia.org/wiki/Cubic_metre_per_secondhttps://en.wikipedia.org/wiki/Volumetric_flowhttps://en.wikipedia.org/wiki/Volumetric_flowhttps://en.wikipedia.org/wiki/Volumetric_flowhttps://en.wikipedia.org/wiki/Cubic_metre_per_secondhttps://en.wikipedia.org/wiki/Velocityhttps://en.wikipedia.org/wiki/Speedhttps://en.wikipedia.org/wiki/Metre_per_secondhttps://en.wikipedia.org/wiki/Volumehttps://en.wikipedia.org/wiki/Cubic_metrehttps://en.wikipedia.org/wiki/Areahttps://en.wikipedia.org/wiki/Square_metrehttps://en.wikipedia.org/wiki/Magnetic_fluxhttps://en.wikipedia.org/wiki/Weber_(Wb)https://en.wikipedia.org/wiki/Radiant_fluxhttps://en.wikipedia.org/wiki/Power_(physics)https://en.wikipedia.org/wiki/Watthttps://en.wikipedia.org/wiki/Electromotive_forcehttps://en.wikipedia.org/wiki/Electrical_potential_differencehttps://en.wikipedia.org/wiki/Voltagehttps://en.wikipedia.org/wiki/Volthttps://en.wikipedia.org/wiki/Magnetic_flux_densityhttps://en.wikipedia.org/wiki/Magnetic_fieldhttps://en.wikipedia.org/wiki/Tesla_(unit)https://en.wikipedia.org/wiki/Solid_anglehttps://en.wikipedia.org/wiki/Steradianhttps://en.wikipedia.org/wiki/Ionizing_radiationhttps://en.wikipedia.org/wiki/Equivalent_dosehttps://en.wikipedia.org/wiki/Sieverthttps://en.wikipedia.org/wiki/Electrical_conductancehttps://en.wikipedia.org/wiki/Siemens_(unit)https://en.wikipedia.org/wiki/Anglehttps://en.wikipedia.org/wiki/Radianhttps://en.wikipedia.org/wiki/Stress_(physics)https://en.wikipedia.org/wiki/Pressurehttps://en.wikipedia.org/wiki/Pascal_(unit)https://en.wikipedia.org/wiki/Reactance_(electronics)https://en.wikipedia.org/wiki/Electrical_impedancehttps://en.wikipedia.org/wiki/Electric_resistancehttps://en.wikipedia.org/wiki/Ohm_(unit)https://en.wikipedia.org/wiki/Weighthttps://en.wikipedia.org/wiki/Forcehttps://en.wikipedia.org/wiki/Newton_(unit)https://en.wikipedia.org/wiki/Illuminancehttps://en.wikipedia.org/wiki/Luxhttps://en.wikipedia.org/wiki/Luminous_fluxhttps://en.wikipedia.org/wiki/Lumen_(unit)https://en.wikipedia.org/wiki/Catalytic_activityhttps://en.wikipedia.org/wiki/Katalhttps://en.wikipedia.org/wiki/Heathttps://en.wikipedia.org/wiki/Mechanical_workhttps://en.wikipedia.org/wiki/Energyhttps://en.wikipedia.org/wiki/Joulehttps://en.wikipedia.org/wiki/Frequencyhttps://en.wikipedia.org/wiki/Hertzhttps://en.wikipedia.org/wiki/Inductancehttps://en.wikipedia.org/wiki/Henry_(unit)https://en.wikipedia.org/wiki/Ionizing_radiationhttps://en.wikipedia.org/wiki/Absorbed_dosehttps://en.wikipedia.org/wiki/Gray_(unit)https://en.wikipedia.org/wiki/Electric_capacitancehttps://en.wikipedia.org/wiki/Faradhttps://en.wikipedia.org/wiki/Temperaturehttps://en.wikipedia.org/wiki/Celsiushttps://en.wikipedia.org/wiki/Quantity_of_electricityhttps://en.wikipedia.org/wiki/Electric_chargehttps://en.wikipedia.org/wiki/Coulombhttps://en.wikipedia.org/wiki/Radioactivityhttps://en.wikipedia.org/wiki/Becquerelhttps://en.wikipedia.org/wiki/SI_base_unithttps://en.wikipedia.org/wiki/Physical_quantityhttps://en.wikipedia.org/wiki/Symbolhttps://en.wikipedia.org/wiki/SIhttps://en.wikipedia.org/wiki/Units_of_measurementhttps://en.wikipedia.org/wiki/Units_of_measurementhttps://en.wikipedia.org/wiki/SI_base_unithttps://en.wikipedia.org/wiki/International_System_of_Units


2/6

metre per second squared m/s2 acceleration ms

2

metre per second cubed m/s jerk, jolt ms3

metre per quartic second m/s4 snap, jounce ms

4

radian per second rad/s angular velocity s1

newton second Ns momentum, impulse mkgs1

newton metre second Nms angular momentum m2kgs

1

newton metre Nm = J/rad torque, moment of force m

2

kg

s

2

newton per second N/s yank mkgs3

reciprocal metre m1 wavenumber m1

kilogram per square metre kg/m2 area density m

2kg

kilogram per cubic metre kg/m3 density, mass density m

3kg

cubic metre per kilogram m3/kg specific volume m

3kg

1

mole per cubic metre mol/m3

amount of substance concentration m3

mol

cubic metre per mole m3/mol molar volume m

3mol

1

joule second Js action m2kgs1

joule per Kelvin J/K heat capacity, entropy m2kgs

2K

1

joule per kelvin mole J/(Kmol) molar heat capacity, molar entropy m2kgs

2K

1mol

1

joule per kilogram kelvin J/(Kkg) specific heat capacity, specific entropy m2s

2K

1

joule per mole J/mol molar energy m2kgs

2mol

1

joule per kilogram J/kg specific energy m2s

2

joule per cubic metre J/m3 energy density m

1kgs

2

newton per metre N/m = J/m2 surface tension, stiffness kgs

2

watt per square metre W/m2

heat flux density, irradiance kgs3

watt per metre Kelvin W/(mK) thermal conductivity m

kg

s

3

K

1

square metre per second m2/s kinematic viscosity, diffusion coefficient m2s1

pascal second Pas = Ns/m2 dynamic viscosity m

1kgs

1

coulomb per square metre C/m2 electric displacement field, polarization vector m

2sA

coulomb per cubic metre C/m3

electric charge density m3

sA

ampere per square metre A/m2

electric current density Am2

siemens per metre S/m conductivity m3

kg1

s3A

2

siemens square metre per mole Sm2/mol molar conductivity kg

-1s

3mol

1A

2

farad per metre F/m permittivity m3

kg1

s4A

2

henry per metre H/m permeability mkgs2

A2

volt per metre V/m electric field strength mkgs3

A1

ampere per metre A/m magnetic field strength Am1

candela per square metre cd/m2 luminance cdm

2

lumen second lms luminous energy cdsrs

lux second lxs luminous exposure cdsrs/m2

coulomb per kilogram C/kg exposure (X and gamma rays) kg1sA

gray per second Gy/s absorbed dose rate m2s

3

ohm metre

m resistivity m

3

kg

s

3

A

2
https://en.wikipedia.org/wiki/Metre_per_second_squaredhttps://en.wikipedia.org/wiki/Accelerationhttps://en.wikipedia.org/wiki/Jerk_(physics)https://en.wikipedia.org/wiki/Jouncehttps://en.wikipedia.org/wiki/Radian_per_secondhttps://en.wikipedia.org/wiki/Angular_velocityhttps://en.wikipedia.org/wiki/Newton_secondhttps://en.wikipedia.org/wiki/Momentumhttps://en.wikipedia.org/wiki/Impulse_(physics)https://en.wikipedia.org/wiki/Angular_momentumhttps://en.wikipedia.org/wiki/Newton_metrehttps://en.wikipedia.org/wiki/Torquehttps://en.wikipedia.org/w/index.php?title=Yank_(physics)&action=edit&redlink=1https://en.wikipedia.org/w/index.php?title=Yank_(physics)&action=edit&redlink=1https://en.wikipedia.org/wiki/Reciprocal_metrehttps://en.wikipedia.org/wiki/Wavenumberhttps://en.wikipedia.org/wiki/Area_densityhttps://en.wikipedia.org/wiki/Kilogram_per_cubic_metrehttps://en.wikipedia.org/wiki/Densityhttps://en.wikipedia.org/wiki/Specific_volumehttps://en.wikipedia.org/wiki/Molar_volumehttps://en.wikipedia.org/wiki/Joule_secondhttps://en.wikipedia.org/wiki/Action_(physics)https://en.wikipedia.org/wiki/Heat_capacityhttps://en.wikipedia.org/wiki/Entropyhttps://en.wikipedia.org/wiki/Specific_heat_capacityhttps://en.wikipedia.org/wiki/Joule_per_molehttps://en.wikipedia.org/wiki/Specific_energyhttps://en.wikipedia.org/wiki/Energy_densityhttps://en.wikipedia.org/wiki/Surface_tensionhttps://en.wikipedia.org/wiki/Stiffnesshttps://en.wikipedia.org/wiki/Irradiancehttps://en.wikipedia.org/wiki/Thermal_conductivityhttps://en.wikipedia.org/wiki/Viscosityhttps://en.wikipedia.org/wiki/Diffusionhttps://en.wikipedia.org/wiki/Pascal_secondhttps://en.wikipedia.org/wiki/Viscosityhttps://en.wikipedia.org/wiki/Electric_displacement_fieldhttps://en.wikipedia.org/w/index.php?title=Polarization_vector&action=edit&redlink=1https://en.wikipedia.org/wiki/Electrical_conductivityhttps://en.wikipedia.org/wiki/Permittivityhttps://en.wikipedia.org/wiki/Permeability_(electromagnetism)https://en.wikipedia.org/wiki/Electric_fieldhttps://en.wikipedia.org/wiki/Magnetic_fieldhttps://en.wikipedia.org/wiki/Candela_per_square_metrehttps://en.wikipedia.org/wiki/Luminancehttps://en.wikipedia.org/wiki/Lumen_secondhttps://en.wikipedia.org/wiki/Luminous_energyhttps://en.wikipedia.org/wiki/Lux_secondhttps://en.wikipedia.org/wiki/Luminous_exposurehttps://en.wikipedia.org/wiki/Ionizing_radiationhttps://en.wikipedia.org/wiki/X-rayhttps://en.wikipedia.org/wiki/Gamma_rayhttps://en.wikipedia.org/wiki/Absorbed_dosehttps://en.wikipedia.org/wiki/Resistivityhttps://en.wikipedia.org/wiki/Resistivityhttps://en.wikipedia.org/wiki/Absorbed_dosehttps://en.wikipedia.org/wiki/Gamma_rayhttps://en.wikipedia.org/wiki/X-rayhttps://en.wikipedia.org/wiki/Ionizing_radiationhttps://en.wikipedia.org/wiki/Luminous_exposurehttps://en.wikipedia.org/wiki/Lux_secondhttps://en.wikipedia.org/wiki/Luminous_energyhttps://en.wikipedia.org/wiki/Lumen_secondhttps://en.wikipedia.org/wiki/Luminancehttps://en.wikipedia.org/wiki/Candela_per_square_metrehttps://en.wikipedia.org/wiki/Magnetic_fieldhttps://en.wikipedia.org/wiki/Electric_fieldhttps://en.wikipedia.org/wiki/Permeability_(electromagnetism)https://en.wikipedia.org/wiki/Permittivityhttps://en.wikipedia.org/wiki/Electrical_conductivityhttps://en.wikipedia.org/w/index.php?title=Polarization_vector&action=edit&redlink=1https://en.wikipedia.org/wiki/Electric_displacement_fieldhttps://en.wikipedia.org/wiki/Viscosityhttps://en.wikipedia.org/wiki/Pascal_secondhttps://en.wikipedia.org/wiki/Diffusionhttps://en.wikipedia.org/wiki/Viscosityhttps://en.wikipedia.org/wiki/Thermal_conductivityhttps://en.wikipedia.org/wiki/Irradiancehttps://en.wikipedia.org/wiki/Stiffnesshttps://en.wikipedia.org/wiki/Surface_tensionhttps://en.wikipedia.org/wiki/Energy_densityhttps://en.wikipedia.org/wiki/Specific_energyhttps://en.wikipedia.org/wiki/Joule_per_molehttps://en.wikipedia.org/wiki/Specific_heat_capacityhttps://en.wikipedia.org/wiki/Entropyhttps://en.wikipedia.org/wiki/Heat_capacityhttps://en.wikipedia.org/wiki/Action_(physics)https://en.wikipedia.org/wiki/Joule_secondhttps://en.wikipedia.org/wiki/Molar_volumehttps://en.wikipedia.org/wiki/Specific_volumehttps://en.wikipedia.org/wiki/Densityhttps://en.wikipedia.org/wiki/Kilogram_per_cubic_metrehttps://en.wikipedia.org/wiki/Area_densityhttps://en.wikipedia.org/wiki/Wavenumberhttps://en.wikipedia.org/wiki/Reciprocal_metrehttps://en.wikipedia.org/w/index.php?title=Yank_(physics)&action=edit&redlink=1https://en.wikipedia.org/wiki/Torquehttps://en.wikipedia.org/wiki/Newton_metrehttps://en.wikipedia.org/wiki/Angular_momentumhttps://en.wikipedia.org/wiki/Impulse_(physics)https://en.wikipedia.org/wiki/Momentumhttps://en.wikipedia.org/wiki/Newton_secondhttps://en.wikipedia.org/wiki/Angular_velocityhttps://en.wikipedia.org/wiki/Radian_per_secondhttps://en.wikipedia.org/wiki/Jouncehttps://en.wikipedia.org/wiki/Jerk_(physics)https://en.wikipedia.org/wiki/Accelerationhttps://en.wikipedia.org/wiki/Metre_per_second_squared


3/6

SI BASE UNITS

The Systme Internationale dUnits (SI)[1]

, orInternational System of Units, defines seven units of measure as a

basic set from which all other SI units are derived. These SI base units and their physical quantities are:

metre forlength (US English: meter)

kilogram formass (note: not the gram)

second fortime

ampere forelectric current

kelvin fortemperature

candela forluminous intensity

mole for the amount of substance.

The SI base quantities form a set of mutually independent dimensions as required by dimensional

analysis commonly employed in science and technology. However, in a given realization of these units they may

well be interdependent, i.e. defined in terms of each other.

The names of SI units are written in lowercase characters (the 'degree Celsius' meets this rule, as 'degree' is the

unit, and 'Celsius' is a modifier). The symbols of units are written in lowercase (e.g. metre has the symbol m), except

that symbols for units named after persons are written with an initial capital letter (e.g., the hertzhas the uppercase

symbol Hz). Many other units, such as the litre (US English: liter), are formally not part of the SI, but are accepted

for use with SI.

The seven SI base units

Name Symbol Measure Current (2005) formal definition [2] Historical origin / justification

metre m length

"The metre is the length of the path travelledby light in vacuum during a time interval of1299,792,458 of a second."17th CGPM (1983, Resolution 1, CR, 97)

110,000,000 of the distance fromthe Earth's equator to the NorthPole measured on thecircumference through Paris.

kilogram

kg mass

"The kilogram is the unit of mass; it is equalto the mass of the international prototype of

the kilogram."3rd CGPM (1901, CR, 70)

The mass of one litre ofwater. Alitre is one thousandth of a cubicmetre.

second S time

"The second is the durationof 9,192,631,770 periods of the radiationcorresponding to the transition between thetwo hyperfine levels of the ground state ofthe caesium 133 atom."13th CGPM (1967/68, Resolution 1; CR,103)"This definition refers to a caesium atom at

rest at a temperature of 0 K."(Added by CIPM in 1997)

The day is divided in 24 hours,each hour divided in 60 minutes,each minute divided in 60seconds.

A second is 1(24 60 60) ofthe day

ampere A electric current

"The ampere is that constant current which,if maintained in two straight parallelconductors of infinite length, of negligiblecircular cross-section, and placed 1 metreapart in vacuum, would produce betweenthese conductors a force equal to 2 10

7newton per metre of length."

The original "InternationalAmpere" was definedelectrochemically as the currentrequired to deposit 1.118milligrams of silver per secondfrom a solution ofsilver nitrate.Compared to the SI ampere, the
http://en.wikipedia.org/wiki/SI_base_unit#cite_note-1http://en.wikipedia.org/wiki/SI_base_unit#cite_note-1http://en.wikipedia.org/wiki/SI_base_unit#cite_note-1http://en.wikipedia.org/wiki/International_System_of_Unitshttp://en.wikipedia.org/wiki/SI_derived_unithttp://en.wikipedia.org/wiki/Metrehttp://en.wikipedia.org/wiki/Lengthhttp://en.wikipedia.org/wiki/Kilogramhttp://en.wikipedia.org/wiki/Masshttp://en.wikipedia.org/wiki/Gramhttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Timehttp://en.wikipedia.org/wiki/Amperehttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Kelvinhttp://en.wikipedia.org/wiki/Temperaturehttp://en.wikipedia.org/wiki/Candelahttp://en.wikipedia.org/wiki/Luminous_intensityhttp://en.wikipedia.org/wiki/Mole_(unit)http://en.wikipedia.org/wiki/Amount_of_substancehttp://en.wikipedia.org/wiki/Dimensional_analysishttp://en.wikipedia.org/wiki/Dimensional_analysishttp://en.wikipedia.org/wiki/Litrehttp://en.wikipedia.org/wiki/Units_accepted_for_use_with_SIhttp://en.wikipedia.org/wiki/Units_accepted_for_use_with_SIhttp://en.wikipedia.org/wiki/SI_base_unit#cite_note-sibro-2http://en.wikipedia.org/wiki/SI_base_unit#cite_note-sibro-2http://en.wikipedia.org/wiki/Metrehttp://en.wikipedia.org/wiki/Lengthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Parishttp://en.wikipedia.org/wiki/Kilogramhttp://en.wikipedia.org/wiki/Masshttp://en.wikipedia.org/wiki/Litrehttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Timehttp://en.wikipedia.org/wiki/Dayhttp://en.wikipedia.org/wiki/Amperehttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Newton_(unit)http://en.wikipedia.org/wiki/Silver_nitratehttp://en.wikipedia.org/wiki/Silver_nitratehttp://en.wikipedia.org/wiki/Newton_(unit)http://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Amperehttp://en.wikipedia.org/wiki/Dayhttp://en.wikipedia.org/wiki/Timehttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Waterhttp://en.wikipedia.org/wiki/Litrehttp://en.wikipedia.org/wiki/Masshttp://en.wikipedia.org/wiki/Kilogramhttp://en.wikipedia.org/wiki/Parishttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Lengthhttp://en.wikipedia.org/wiki/Metrehttp://en.wikipedia.org/wiki/SI_base_unit#cite_note-sibro-2http://en.wikipedia.org/wiki/Units_accepted_for_use_with_SIhttp://en.wikipedia.org/wiki/Units_accepted_for_use_with_SIhttp://en.wikipedia.org/wiki/Litrehttp://en.wikipedia.org/wiki/Dimensional_analysishttp://en.wikipedia.org/wiki/Dimensional_analysishttp://en.wikipedia.org/wiki/Amount_of_substancehttp://en.wikipedia.org/wiki/Mole_(unit)http://en.wikipedia.org/wiki/Luminous_intensityhttp://en.wikipedia.org/wiki/Candelahttp://en.wikipedia.org/wiki/Temperaturehttp://en.wikipedia.org/wiki/Kelvinhttp://en.wikipedia.org/wiki/Electric_currenthttp://en.wikipedia.org/wiki/Amperehttp://en.wikipedia.org/wiki/Timehttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Gramhttp://en.wikipedia.org/wiki/Masshttp://en.wikipedia.org/wiki/Kilogramhttp://en.wikipedia.org/wiki/Lengthhttp://en.wikipedia.org/wiki/Metrehttp://en.wikipedia.org/wiki/SI_derived_unithttp://en.wikipedia.org/wiki/International_System_of_Unitshttp://en.wikipedia.org/wiki/SI_base_unit#cite_note-1


4/6

9th CGPM (1948) difference is 0.015%.

kelvin K thermodynamic

temperature

"The kelvin, unit of thermodynamictemperature, is the fraction 1273.16 of thethermodynamic temperature of the triple

point of water."

13th CGPM (1967/68, Resolution 4; CR,

104)"This definition refers to water having theisotopic composition defined exactly by thefollowing amount of substance ratios: 0.000155 76 mole of

2H per mole of

1H, 0.000 379

9 mole of17O per mole of16O, and 0.002005 2 mole of

18O per mole of

16O."

(Added by CIPM in 2005)

The Celsius scale: the Kelvin scale

uses the degree Celsius for its unitincrement, but is a thermodynamicscale (0 K is absolute zero).

mole Molamount ofsubstance

"1. The mole is the amount of substance ofa system which contains as manyelementary entities as there are atoms in0.012 kilogram of carbon 12; its symbol is'mol.'

2. When the mole is used, the elementary

entities must be specified and may be

atoms, molecules, ions, electrons, other

particles, or specified groups of such

particles."

14th CGPM (1971, Resolution 3; CR, 78)

"In this definition, it is understood that

unbound atoms of carbon 12, at rest and in

their ground state, are referred to."

(Added by CIPM in 1980)

Atomic weight ormolecular

weight divided by the molar mass

constant, 1 g/mol.

candela Cdluminousintensity

"The candela is the luminous intensity, in agiven direction, of a source that emitsmonochromatic radiation offrequency 54010

12hertz and that has a

radiant intensity in that direction of 1/683watt persteradian."

16th CGPM (1979, Resolution 3; CR, 100)

The candlepower, which is based

on the light emitted from a burningcandle of standard properties.

RULES FOR ROUNDING OFF NUMBERS

CASE A:In rounding off numbers, the last figure kept should be unchanged if the first figure dropped is less than 5.For example, if only one decimal is to be kept, then 6.422 becomes 6.4.

CASE B:In rounding off numbers, the last figure kept should be increased by 1 if the first figure dropped is greater than 5.

For example, if only two decimals are to be kept, then 6.4872 becomes 6.49. Similarly, 6.997 becomes 7.00.

CASE C:In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero orif there are nofigures after the 5, then the last figure kept should be unchanged if that last figure is even.For example, if only one decimal is to be kept, then 6.6500 becomes 6.6.

For example, if only two decimals are to be kept, then 7.485 becomes 7.48.
http://en.wikipedia.org/wiki/Kelvinhttp://en.wikipedia.org/wiki/Thermodynamic_temperaturehttp://en.wikipedia.org/wiki/Thermodynamic_temperaturehttp://en.wikipedia.org/wiki/Triple_pointhttp://en.wikipedia.org/wiki/Triple_pointhttp://en.wikipedia.org/wiki/Celsius_scalehttp://en.wikipedia.org/wiki/Absolute_zerohttp://en.wikipedia.org/wiki/Mole_(unit)http://en.wikipedia.org/wiki/Amount_of_substancehttp://en.wikipedia.org/wiki/Amount_of_substancehttp://en.wikipedia.org/wiki/Atomic_weighthttp://en.wikipedia.org/wiki/Molecular_weighthttp://en.wikipedia.org/wiki/Molecular_weighthttp://en.wikipedia.org/wiki/Molar_mass_constanthttp://en.wikipedia.org/wiki/Molar_mass_constanthttp://en.wikipedia.org/wiki/Candelahttp://en.wikipedia.org/wiki/Luminous_intensityhttp://en.wikipedia.org/wiki/Luminous_intensityhttp://en.wikipedia.org/wiki/Steradianhttp://en.wikipedia.org/wiki/Candlepowerhttp://en.wikipedia.org/wiki/Candlepowerhttp://en.wikipedia.org/wiki/Steradianhttp://en.wikipedia.org/wiki/Luminous_intensityhttp://en.wikipedia.org/wiki/Luminous_intensityhttp://en.wikipedia.org/wiki/Candelahttp://en.wikipedia.org/wiki/Molar_mass_constanthttp://en.wikipedia.org/wiki/Molar_mass_constanthttp://en.wikipedia.org/wiki/Molecular_weighthttp://en.wikipedia.org/wiki/Molecular_weighthttp://en.wikipedia.org/wiki/Atomic_weighthttp://en.wikipedia.org/wiki/Amount_of_substancehttp://en.wikipedia.org/wiki/Amount_of_substancehttp://en.wikipedia.org/wiki/Mole_(unit)http://en.wikipedia.org/wiki/Absolute_zerohttp://en.wikipedia.org/wiki/Celsius_scalehttp://en.wikipedia.org/wiki/Triple_pointhttp://en.wikipedia.org/wiki/Triple_pointhttp://en.wikipedia.org/wiki/Thermodynamic_temperaturehttp://en.wikipedia.org/wiki/Thermodynamic_temperaturehttp://en.wikipedia.org/wiki/Kelvin


5/6

CASE D:In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero orif there are nofigures after the 5, then the last figure kept should be increased by 1 if that last figure is odd.For example, if only two decimals are to be kept, then 6.755000 becomes 6.76.

For example, if only two decimals are to be kept, 8.995 becomes 9.00.

CASE E:In rounding off numbers, if the first figure dropped is 5, and there are any figures following the five that arenotzero,

then the last figure kept should be increased by 1.For example, if only one decimal is to be kept, then 6.6501 becomes 6.7.

For example, if only two decimals are to be kept, then 7.4852007 becomes 7.49.

NUMBERNumber of decimalplaces desired

Last figureto be kept

First figureto be dropped

Last figurekept and/or number becomes

6.422 1 6.4 6.42 6.4

6.4872 2 6.48 6.487 6.49

6.997 2 6.99 6.997 7.00

6.6500 1 6.6 6.65 6.6

7.485 2 7.48 7.485 7.48

6.755000 2 6.75 6.755 6.76

8.995 2 8.99 8.995 9.00

6.6501 1 6.6 6.65 6.7

7.4852007 2 7.48 7.485 7.49

Rule One. Determine what your rounding digit is and look to the right side of it. If the digit is 0, 1, 2, 3, or 4 do not

change the rounding digit. All digits that are on the right hand side of the requested rounding digit will become 0.

Rule Two. Determine what your rounding digit is and look to the right of it. If the digit is 5, 6, 7, 8, or 9, your

rounding digit rounds up by one number. All digits that are on the right hand side of the requested rounding digit will

become 0.

Rounding with decimals: When rounding numbers involving decimals, there are 2 rules to remember:

Rule One Determine what your rounding digit is and look to the right side of it. If that digit is 4, 3, 2, or 1, simply drop

all digits to the right of it.

Rule Two Determine what your rounding digit is and look to the right side of it. If that digit is 5, 6, 7, 8, or 9 add one

to the rounding digit and drop all digits to the right of it.

Rule Three:Some teachers prefer this method:

This rule provides more accuracy and is sometimes referred to as the 'Banker's Rule'. When the first digit dropped is

5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e. round off to

the nearest even digit). E.g., 2.315 and 2.325 are both 2.32 when rounded off to the nearest hundredth.


6/6

What is a "significant figure"?

The number of significant figures in a result is simplythe number of figures that are known with somedegree of reliability. The number 13.2 is said to have 3significant figures. The number 13.20 is said to have 4significant figures.

Rules for deciding the number of significant

figures in a measured quantity:

(1) All nonzero digits are significant:

1.234 g has 4 significant figures,1.2 g has 2 significant figures.

(2) Zeroes between nonzero digits are significant:

1002 kg has 4 significant figures,3.07 mL has 3 significant figures.

(3) Leading zeros to the left of the first nonzero digitsare not significant; such zeroes merely indicate theposition of the decimal point:

0.001oC has only 1 significant figure,

0.012 g has 2 significant figures.

(4) Trailing zeroes that are also to the right of adecimal point in a number are significant:

0.0230 mL has 3 significant figures,0.20 g has 2 significant figures.

(5) When a number ends in zeroes that are not to theright of a decimal point, the zeroes are not necessarilysignificant:

190 miles may be 2 or 3 significant figures,50,600 calories may be 3, 4, or 5 significant figures.

The potential ambiguity in the last rule can be avoidedby the use of standard exponential, or "scientific,"notation. For example, depending on whether thenumber of significant figures is 3, 4, or 5, we would

write 50,600 calories as:

5.06 104

calories (3 significant figures)5.060 10

4calories (4 significant figures), or

5.0600 104

calories (5 significant figures).

By writing a number in scientific notation, the numberof significant figures is clearly indicated by the numberofnumerical figures in the 'digit' term as shown bythese examples. This approach is a reasonableconvention to follow.

Rules for mathematical operations

In carrying out calculations, the general rule is that theaccuracy of a calculated result is limited by the leastaccurate measurement involved in the calculation.

(1) In addition and subtraction, the result is rounded offto the last common digit occurring furthest to the rightin all components. Another way to state this rule is as

follows: in addition and subtraction, the result isrounded off so that it has the same number of digits asthe measurement having the fewest decimal places(counting from left to right). For example,

100 (assume 3 significant figures) + 23.643 (5

significant figures) = 123.643,

which should be rounded to 124 (3 significant figures).Note, however, that it is possible two numbers have nocommon digits (significant figures in the same digitcolumn).

(2) In multiplication and division, the result should berounded off so as to have the same number ofsignificant figures as in the component with the leastnumber of significant figures. For example,

3.0 (2 significant figures ) 12.60 (4 significant

figures) = 37.8000

which should be rounded to 38 (2 significant figures).

Rules for rounding off numbers

(1) If the digit to be dropped is greater than 5, the lastretained digit is increased by one. For example,

12.6 is rounded to 13.

(2) If the digit to be dropped is less than 5, the lastremaining digit is left as it is. For example,


(3) If the digit to be dropped is 5, and if any digitfollowing it is not zero, the last remaining digit isincreased by one. For example,


(4) If the digit to be dropped is 5 and is followed onlyby zeroes, the last remaining digit is increased by oneif it is odd, but left as it is if even. For example,

11.5 is rounded to 12,12.5 is rounded to 12.

This rule means that if the digit to be dropped is 5followed only by zeroes, the result is always roundedto the even digit. The rationale for this rule is to avoidbias in rounding: half of the time we round up, half thetime we round down.

Documents

Si Derived Units