SI Units: The International System of Units for Measurement, Study notes of History

An overview of the si system of units, an international standard for measurement adopted by various national and international organizations. The seven base units, two supplementary units, derived units, prefixes, and rules for writing unit symbols and values. It also includes conversions from cgs units to si units.

Typology: Study notes

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Appendix A: SI Units
‘‘SI’ is an abbreviation for Le Syste
`me International d’Unite
´s, an international system of units
adopted by many national and international authorities, associations, professional societies, and agencies.
SI is closely related to but not identical with the former cgs, mks, and mksa systems of metric units.
Official information, development history, and more detail on SI can be found in Bureau of Standards
Special Publication 330 1974and in the SEG Subcommittee on Metrification 1981publication.
SI is based on seven base units listed in Table 1 and two supplementary units the last two.
SI derived units are formed by combining the base and supplementary units. Some of the derived
units are listed in Table 2.
Table 3 shows how larger or smaller units can be made by adding prefixes. When prefixes are used,
the first syllable is accented. Note that k and M stand for 10 3and 106, whereas M and MM or m and
mmare sometimes used in the oil industry for designating thousands and millions of gas volumes.
Prefixes are raised to the power of the unit employed; for example, km3means cubic kilometers, not
thousands of cubic meters. Prefixes are not compounded GW rather than kMW.
SEG allows the forms in Table 4 in addition to those in Tables 1 to 3.
Table 5 relates cgs electromagnetic and electrostatic units to SI units; see also Figure E-8. Figure M-1
relates cgs and SI magnetic units.
Rules about writing units
Symbols are written in Roman not italicstype. They are never pluralized.
Unit names, including prefixes, are not capitalized except at the beginning of a sentence or in titles.
Unit names are pluralized in the usual manner, as 100 meters, 70 henries, except for lux, hertz, and
siemens. Fractional values require the singular form.
Periods are not used after symbols, that is, symbols are not abbreviations.
Symbols are lower case except when named for a person exception: L for liter.
A space separates a numerical value and the unit symbol except for °C; thus, 10 m, 0.112 s,
1.5 g/cm3, 20°C. A hyphen separates value and symbol when used as an adjective; thus, 35-mm film. No
space separates a prefix and the symbol; thus, ms for milliseconds, kW for kilowatt.
The symbols ‘‘/’ or ‘.’’ are used to indicate the compounding of symbols for example, km/s or N.m
for kilometers per second and newton-meter, but are not used when units are written out. Where
symbols are compounded, parentheses should be used to avoid ambiguity, as W/m.k. ‘‘P’ is not
acceptable as an abbreviation for ‘‘per.’’ ‘‘Per’’ should not be compounded; thus, ‘‘meters per second
squared,’’ not ‘‘meters per second per second.’ Userather than for products of numbers; thus
6.25, not 6.2.5. A space should be used on each side of symbols for multiplication, addition, subtrac-
tion, convolution ,,,*and for the division symbol but not for /.
Numbers with many decimal places should be grouped by threes separated by a space rather than by
a comma which Europeans read as a decimal point; thus, 4 720 525 or 0.528 75. For numbers smaller
than one, a zero should be shown in the units place. A space is not necessary for four-digit numbers.
403
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Appendix A: SI Units

‘‘SI’’ is an abbreviation for Le Syste`me International d’Unite´s, an international system of units

adopted by many national and international authorities, associations, professional societies, and agencies.

SI is closely related to but not identical with the former cgs, mks, and mksa systems of metric units.

Official information, development history, and more detail on SI can be found in Bureau of Standards

Special Publication 330  1974  and in the SEG Subcommittee on Metrification  1981  publication.

SI is based on seven base units listed in Table 1 and two supplementary units the last two.

SI derived units are formed by combining the base and supplementary units. Some of the derived

units are listed in Table 2.

Table 3 shows how larger or smaller units can be made by adding prefixes. When prefixes are used,

the first syllable is accented. Note that k and M stand for 10 3 and 10 6 , whereas M and MM or m and

mm are sometimes used in the oil industry for designating thousands and millions of gas volumes.

Prefixes are raised to the power of the unit employed; for example, km 3 means cubic kilometers, not

thousands of cubic meters. Prefixes are not compounded GW rather than kMW.

SEG allows the forms in Table 4 in addition to those in Tables 1 to 3.

Table 5 relates cgs electromagnetic and electrostatic units to SI units; see also Figure E-8. Figure M-

relates cgs and SI magnetic units.

Rules about writing units

Symbols are written in Roman not italics type. They are never pluralized.

Unit names, including prefixes, are not capitalized except at the beginning of a sentence or in titles.

Unit names are pluralized in the usual manner, as 100 meters, 70 henries, except for lux, hertz, and

siemens. Fractional values require the singular form.

Periods are not used after symbols, that is, symbols are not abbreviations.

Symbols are lower case except when named for a person exception: L for liter.

A space separates a numerical value and the unit symbol except for °C; thus, 10 m, 0.112 s,

1.5 g/cm 3 , 20°C. A hyphen separates value and symbol when used as an adjective; thus, 35-mm film. No

space separates a prefix and the symbol; thus, ms for milliseconds, kW for kilowatt.

The symbols ‘‘/’’ or ‘‘.’’ are used to indicate the compounding of symbols for example, km/s or N.m

for kilometers per second and newton-meter, but are not used when units are written out. Where

symbols are compounded, parentheses should be used to avoid ambiguity, as W/m.k. ‘‘P’’ is not

acceptable as an abbreviation for ‘‘per.’’ ‘‘Per’’ should not be compounded; thus, ‘‘meters per second

squared,’’ not ‘‘meters per second per second.’’ Use  rather than • for products of numbers; thus

6.25, not 6.2.5. A space should be used on each side of symbols for multiplication, addition, subtrac-

tion, convolution , , , * and for the division symbol  but not for /.

Numbers with many decimal places should be grouped by threes separated by a space rather than by

a comma which Europeans read as a decimal point; thus, 4 720 525 or 0.528 75. For numbers smaller

than one, a zero should be shown in the units place. A space is not necessary for four-digit numbers.

403

Squared or cubed should follow unit names except for areas and volumes; thus, meter per second

squared, square meter, watt per cubic meter.

The spellings metre and litre are preferred but meter and liter are the official U.S. forms of spelling.

The use of liter as a cubic decimeter is discouraged.

Table 1. SI base and supplementary units. Quantity SI unit symbol Length meter or metre m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temperature kelvin K Amount of substance mole mol Luminous intensity candela cd Plane angle radian rad Solid angle steradian sr

Note that the kilogram is not a unit of force (weight). The word weight is often ambiguous and its use should be avoided. The temperature unit kelvin is not degree kelvin.

Table 2. SI derived units.

Quantity Derived unit, symbol Quantity Derived unit, symbol

Absorbed dose gray, GyJ/kg Luminous flux lumen, lmcd.sr Acceleration meters per second Magnetizing force ampere per meter, squared, m/s 2 A/m Activity (of radionuclides) becquerel, Bql/s Magnetic flux weber, WbV.s Angular acceleration radian per second Magnetic flux density (^) tesla, TWb/m^2 squared, rad/s 2 Potential difference volt, VW/A Angular velocity radian per second, Power watt, WJ/s rad/s Pressure (^) pascal, PaN/m^2 Area square meter, m 2 Quantity of electricity coulomb, CA.s Density kilogram per cubic Quantity of heat joule, JN.m meter, kg/m 3 Radiant flux watt, WJ/s Electric capacitance farad, FA.s/V Radiant intensity watt per steradian, C/V W/sr Electric charge coulomb, CA/s Specific heat capacity joule per kilogram kel- Electrical conductance siemens, SA/V vin, J/kg.K Electric field strength volt per meter, V/m Stress (^) pascal, PaN/m^2 Electric inductance henry, HV.s/A Thermal conductivity watt per meter kelvin, Wb/A W/m.K Electric potential volt, VW/A Torque newton meter (not Electric resistance ohm, Ω V/A joule) Electromotive force volt, VW/A Velocity meter per second, m/s Energy joule, JN.m Viscosity, dynamic pascal second, Pa.s Entropy joule per kelvin, J/K Viscosity, kinematic square meter per sec- Force (^) newton, Nkg.m/s^2 ond, m 2 /s Frequency hertz, Hzl/s Voltage volt, VW/A Illuminance (^) lux, lxlm/m 2 Volume cubic meter, m 3 Luminance candela per square Wavenumber per meter, l/m meter, cd/m^2 Work joule, JN.m

Appendix A 404