A Concise Summary Of The International System Of Units (Page 3 of 4) in pdf

The sievert is also used for the quantities directional dose

The use of a coherent set of units has technical advantages (see

equivalent and personal dose equivalent.

the SI Brochure). However the use of the preﬁxes is convenient

The last four special names for units in Table 4 were

because it avoids the need to use factors of 10

to express the

adopted speciﬁcally to safeguard measurements related to

values of very large or very small quantities. For example, the

human health.

length of a chemical bond is more conveniently given in nano-

metres, nm, than in metres, m, and the distance from London

For each quantity, there is only one SI unit (although it may

to Paris is more conveniently given in kilometres, km, than in

often be expressed in different ways by using the special names).

metres, m.

However the same SI unit may be used to express the values of

The kilogram, kg, is an exception, because although it is a base

several different quantities (for example, the SI unit J/K may be

unit the name already includes a preﬁx, for historical reasons.

used to express the value of both heat capacity and entropy). It

Multiples and sub-multiples of the kilogram are written by

is therefore important not to use the unit alone to specify the

combining preﬁxes with the gram: thus we write milligram, mg,

quantity. This applies both to scientiﬁc texts and also to meas-

not microkilogram, µkg.

uring instruments (i.e. an instrument read-out should indicate

both the quantity concerned and the unit).

Units outside the SI

Dimensionless quantities, also called quantities of dimension

The SI is the only system of units that is universally recognized,

one, are usually deﬁned as the ratio of two quantities of the

so that it has a distinct advantage in establishing an international

same kind (for example, refractive index is the ratio of two

dialogue. Other units, i.e. non-SI units, are generally deﬁned in

speeds, and relative permittivity is the ratio of the permittivity

terms of SI units. The use of the SI also simpliﬁes the teaching

of a dielectric medium to that of free space). Thus the unit of

of science. For all these reasons the use of SI units is recom-

a dimensionless quantity is the ratio of two identical SI units,

mended in all ﬁelds of science and technology.

and is therefore always equal to one. However in expressing

Nonetheless some non-SI units are still widely used. A few, such

the values of dimensionless quantities the unit one, 1, is not

as the minute, hour and day as units of time, will always be used

written.

because they are so deeply embedded in our culture. Others are

used for historical reasons, to meet the needs of special interest

Decimal multiples and sub-multiples of SI units

groups, or because there is no convenient SI alternative. It will

A set of preﬁxes have been adopted for use with the SI units,

always remain the prerogative of a scientist to use the units that

in order to express the values of quantities that are either much

are considered to be best suited to the purpose. However when

larger than or much smaller than the SI unit used without any

non-SI units are used, the conversion factor to the SI should

preﬁx. The SI preﬁxes are listed in Table 5. They may be used

always be quoted. A few non-SI units are listed in Table 6

with any of the base units and with any of the derived units

below with their conversion factors to the SI. For a more

with special names.

complete list, see the SI Brochure, or the BIPM website.

Table 5 The SI preﬁxes

Table 6 A few non-SI units

Factor

Name

Symbol

Factor

Name

Symbol

Quantity

Unit

Symbol

Relation to SI

deca

−1

deci

time

minute

min

1 min = 60 s

hecto

−2

centi

hour

1 h = 3600 s

kilo

milli

day

1 d = 86 400 s

−3

mega

micro

volume

litre

L or l

1 L = 1 dm

−6

giga

−9

nano

mass

tonne

1 t = 1000 kg

1 eV ≈ 1.602 × 10

tera

−12

pico

energy

electronvolt

−19

peta

−15

femto

pressure

bar

1 bar = 100 kPa

1 mmHg ≈ 133.3 Pa

exa

−18

atto

millimetre

mmHg

of mercury

zetta

−21

zepto

length

ångström

1 Å = 10

−10

yotta

−24

yocto

nautical mile M

1 M = 1852 m

force

dyne

dyn

1 dyn = 10

−5

When the preﬁxes are used, the preﬁx name and the unit name

are combined to form a single word, and similarly the preﬁx

energy

erg

1 erg = 10

−7

symbol and the unit symbol are written without any space to

form a single symbol, which may itself be raised to any power.

Symbols for units begin with a capital letter when they are

For example, we may write: kilometre, km; microvolt, µV;

named after an individual (for example, ampere, A; kelvin, K;

femtosecond, fs; 50 V/cm = 50 V (10

−2

−1

= 5000 V/m.

hertz, Hz; coulomb, C). Otherwise they always begin with a

When the base units and derived units are used without any

lower case letter (for example, metre, m; second, s; mole, mol).

preﬁxes, the resulting set of units is described as being coherent.

The symbol for the litre is an exception: either a lower case

A Concise Summary Of The International System Of Units Page 3

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