International System of Units (SI) (Metrology)

1.12.
It is the system established in 1960 by the (CGPM) General Conference of Weights and
Measures and abbreviated as SI (System International d’unites) in all languages. In India, we
switched over to metric system of Weights and Measures conforming to SI units by an Act of
Parliament No. 89, in 1956. This SI like traditional metric system, is based on decimal arithmetic.
For each physical quantity, units of different sizes are formed by multiplying or dividing a single
base value by powers of 10. Obviously this offers great advantage because the changes can be made
very simply by adding zeros or shifting decimal point. In the metric system we have been following
so far, this simplicity of a series of units linked by powers of 10 is limited to plain quantities like
length, and this simplicity is lost when more complex units like energy etc. are encountered. For
example energy is now represented by several units like kgm, H.P., kW etc. In contrast the SI
provides only one basic unit for each physical quantity, and universality is thus achieved. This
system in superior to other systems and also more convenient as it is coherent, rational and
comprehensive.
The SI is a coherent system, in the sense that the product or quotient of any two unit
quantities in the system is the unit of the resultant quantity, e.g. if unit of length is metre, then
unit of area will be square metre and not acres or begas etc. It is rational system since it has absorbed
in itself the rationalised MKSA system. It is also comprehensive because its seven base units cover
all disciplines.
The seven base SI units established by the General Conference of Weights and Measures
are given on next page and SI units having special names are given below.


SI UNITS HAVING SPECIAL NAMES
Physical quantity Name of unit Unit symbol
Force newton N = kg m/s2
Work, energy, quantity of heat joule J = Nm
Power watt W = J/s
Electric charge coulomb C = A.s
Electric potential volt V = W/A
Electric capacitance farad F = C/V
Electric resistance ohm Q = V/A
Electric conductance siemen S = A/V
Magnetic flux weber Wb=Vxs
Inductance henry H = V.s/A
Luminous flux lumen lm = cd.sr
Magnetic flux density tesla T = Wb/m2
Illumination lux lx = lm/m2
Frequency hertz Hz = cycles
Pressure pascal Pa = N/m2
s.
No.
Physical
Quantity
Name of
unit
Unit
symbol
Base of Definition Definition
1. Length metre m Wavelength of red light in Kryp-
ton 86
1,650,673.73 wavelengths in
vacuo of the radiation correspond-
ing to the transition between the
energy levels 2p 10 and 5d5 of the
Krypton 86 atom.
2. Time second s Cycles of radiation of cesium The duration of 9,192,631,770
periods of the radiation cor-
responding to the transition be-
tween the two hyperfine levels of
the ground state of the cesium-
133 atom.
3. Mass kilogram kg Platinum-cylinder prototype Mass of the International
prototype which is in the custody
of Bureau International des Poids
et Mesures (BIPM) at Sevres,
near Paris.
4. Temperature kelvin K Absolute zero and water The fraction 1/273.16 of the ther-
modynamic temperature of the
triple point of water.
5. Electric
current
ampere A Force between two conducting
wires
The constant current which, if
maintained in two parallel recti-
linear conductors of infinite
length, of negligible circular
cross-section, and placed at a dis-
tance one metre apart in vacuum
would produce between these con-
ductors a force equal to 2 x 10~7
N/m length.
6. Luminous
intensity
candela cd Intensity of an area of platinum The luminous intensity, in the
perpendicular direction, of a sur-
face of 1/600,000 square metre of
a black body at the temperature
of freezing platinum under a pres-
sure of 101,325 newtons per
square metre.
7. Quantity of
substance
mole mol Amount of atoms in carbon 12 The amount of substance of a sys-
tem which contains as many
elementary entities as there are
atoms in 0.012 kilogram of carbon
12.

Other physical quantities are derived from these basic units. For example, volume is cubic metre (m3),
speed is metre per second (m/s), force is mass-metres per square second (kg m/sec2). Realising that some derived
units may be ccmpex array of base units, some units have been given special names. They are given on
page 24.
SI also recommends the use of supplementary units, the only authorised supplementary
units being measures for plane and spherical angles. Though these could be expressed by base units
but have been available as a convenience to users. Plane angles are represented by radians and
solid angles by steradians.
Decimal multiples and sub-multiples of the SI units are formed by means of the prefixes
given below, which represent the numerical factors shown :

Multiplication factor Prefix SI Symbol
1012 tera T
109 giga G
166 mega M
103 kilo k
102 hecto* h
101 deka da
lO”1 deci* d
io-2 centi* c
IO”3 milli m
IO”6 micro
1(T9 nano n
i<r12 pico P
IO”15 fern to f
IO”18 atto a

*To be avoided where possible.
The two major advantages of coherency of SI units are (i) same system and unit of
measurement are used regardless of industry, trade, or discipline ; and (ii) minimum of conversion
factors are needed (other than powers of 10).
In connection with SI units, some rules of style, abbreviations, writing, and drafting practices
are applied, some of which are described below :
(a) No dots, commas, 4^c, are used after SI symbols except at the end of sentences. For
example 32 metres will be written as 32 m but when written as 32 m. is not correct.
(b) Plurals are never used in connection with SI unit symbols, for example 32 metres will be
written as 32 m and not as 32 ms which would mean 32 milli-seconds.
(c) Decimal fractions are always started with 0. For example, half metre will be written as
0.5 m and not as .5 m.
(d) Multiplication or times sign is ‘.’ This is used between the number to be multiplied and
between unit symbols in derived units where two unit symbols adjoin for the purpose of clarity, e.g.
unit of torque may be written as m.N (metre newton) which if written as mN can be misunderstood
as millinewton.
(e) All symbols and prefixes are lowercase letters, except symbols derived from proper names,
like W for watt, M, G and T for the largest three power-of-10 prefixes. All symbols should be used
as they are to avoid any confusion.
(f) All units may be written either in full or using the agreed symbols. There is only one
acceptable symbol in all languages for a metric unit. For example KILOGRAM be written as kg and
not as kgm or kg, or kgr. etc.
(g) The product of two or more units is preferably indicated by a dot which can be dispensed
with when there is no risk of confusion with another unit symbol e.g., 63 N.m or 63 Nm is correct
but not 63 mN.
(h) There is a mixture of capital and lower case letters in the symbols for the prefixes, but
the full names of the prefixes commence with lower case letters only, e.g. 200 MW is written is 200
megawatts.
(i) No degree mark (°) is used with kelvin, the unit of temperature. A temperature interval
can also be expressed in degree Celsius.
(J) Double prefixes should not be used e.g. one kilo Megawatt may not be written as kMW,
but as GW.
(k) Algebraic symbols representing quantities are written in italics while symbols for units
are written in upright characters.
(I) The expression “per” in symbols of derived units is always indicated by a fraction line as
m/s of but word “per” or letter “p” should not be used for this purpose.
(m) Always leave one space between numerical value and the symbol. For example, 92 N is
commitment 92N is not.
(n) Only the numerator should be multiplied by powers of 10 in compound derived units and
the denominator should always remain the base unit.
For example 0.032 m/s may be put as 32 mm/s and not as 0.000032 m/ms. (meter per
millisecond).
(o) Numbers may be grouped in clusters of three in both directions from the decimal mark,
and gap may be given for clarity and comma should not be used there.
e.g. 153297.3 m may be written as 153 297.3 m and not 153,297.3 m. A sequence of four
figures is generally not broken in groups.
(p) Units with names of scientists should be capitalised when written in full.
(q) According to SI recommendations, litre is a special name given to cubic decimetre and
the world litre should not be used for expressing results of high precision volume measurements.
(r) Some units which though strictly incompatible with SI units, have been allowed initially,
like km/hr, rev/min.
(s) The appropriate integers, multiples and sub-multiples to which a unit is to be expressed
is selected in such a manner that the numerical value to be expressed is between 0.1 and 1000.
(t) Figures are written in groups of three to the left and to the right of the decimal sign.
(u) Thousands are separated by a space and NOT by a comma e.g. 6000 000 kl is correct but
6,000,000 kl is not correct.
(v) In some countries, a point (dot) is used as the decimal marker, and in some countries a
comma is used ; both are understood internationally.

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