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Scientific Notation
Since the Encyclopedia is a work of science, in the articles it was necessary to follow the scientific style of using symbols, abbreviations, and exact names. This section discusses the more frequently used conventions in the Encyclopedia and includes tables for convenient reference. The relation between the three primary measurement systems—U.S. Customary, metric, and International—is also clarified.
U.S. Customary System and the metric system
Scientists and engineers have been using two major systems of units in measurement.
These are commonly called the U.S. Customary System (inherited from the British
Imperial System) and the metric system.
In the U.S. Customary System the units yard and pound with their divisions, such
as the inch, and multiples, such as the ton, are basic. The metric system was developed
during the eighteenth century and has been adopted for general use by most countries.
It is used nearly everywhere for precise measurements in science. The meter and
kilogram with their multiples, such as the kilometer, and fractions, such as the
gram, are basic to the metric system.
In the U.S. Customary System, units of the same kind are related almost at random.
For example, there are the units of length, the inch, yard, and mile. In the metric
system the relationships between units of the same kind are strictly decimal (millimeter,
meter, and kilometer).
However, to complicate matters, in scientific writing there is no uniformity within
each of these two systems as to the choice of units for the same quantities. For
example, the hour or the second, the foot or the inch, and the centimeter or the
millimeter could be chosen by a scientist as the unit of measurement for the quantities
time and length.
Introduction of the International System
To simplify matters and to make communication more understandable, an internationally
accepted system of units has come into use. This is termed the International System
of Units, which is abbreviated SI in all languages (from the French Systéme International
d'Unités).
Fundamentally the system is metric with the base units derived from scientific formulas
or natural constants. For example, the meter in the SI is defined as the length
of the path traveled by light in vacuum during a time interval of 1/299 792 458
of a second.
The second in the SI is defined as the duration of 9 192 631 770 periods of the
radiation corresponding to the transition between two hyperfine levels of the ground
state of the cesium-133 atom.
Interestingly, the kilogram, the SI unit of mass, is still the mass of the kilogram
kept at Sévres, France. However, it is possible that eventually the unit will be
redefined in terms of atomic mass.
Although the SI is increasingly used by scientists and engineers, there are some
other units in everyday use which will probably remain, for example, minute, hour,
day, degree (angle), and liter. The point should be made, however, that these terms
will not be employed in a scientific context if the SI is fully adopted.
Because of their extremely common use among scientists, several units are still
permitted in conjunction with SI units, for example, the electronvolt, rad, roentgen,
barn, and curie. In time their usage might be phased out.
One further point is that in October 1967 the Thirteenth General Conference of Weights
and Measures decided to name the SI unit of thermodynamic temperature "kelvin" (symbol
K) instead of "degree Kelvin" (symbol °K). For example, the notation is 273 K and
not 273 ° K. The base units and derived units of the SI are shown in Tables
1 and
2.
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Base units of the International System
|
|
Quantity
|
Name of unit
|
Unit symbol
|
|
length
|
meter |
m
|
|
mass
|
kilogram
|
kg
|
|
time
|
second |
s |
|
electric current |
ampere |
A |
|
temperature |
kelvin |
K |
|
luminous intensity |
candela |
cd |
|
amount of substance |
mole |
mol |
In the SI the prefixes differ from a unit in steps of 10 3 . A list of
prefix terms, symbols, and their factors is given in Table 3. Some examples
of the use of these prefixes follow:
|
1000 m = |
1 kilometer |
= 1 km |
|
1000 V = |
1 kilovolt
|
= 1 kV |
1 000000
= |
1 megohm |
= 1M
|
|
0.000 000 001 s = |
1 nanosecond
|
= 1 ns |
Only one prefix is to be employed
for a unit. For example:
|
1000 kg = |
1 Mg
|
not 1 kkg |
|
10–9 s = |
1 ns |
not 1 mµ s |
|
1 000 000 m = |
1 Mm
|
not 1 kkm |
Also, when a unit is raised to a power, the power applies to the whole unit including
the prefix. For example:
km 2 = (km) 2 = (1000 m) 2 = 10 6 m 2
not 1000 m 2
Some common units defined in terms of SI units are given in Table 4 (the definitions
in the fourth column are exact).
Conversion factors for the measurement systems
The Encyclopedia has retained the U.S. Customary and metric systems, but has incorporated
SI units. Conversion factors between the three measurement systems are given in
Table 5
for some prevalent units; in each of the subtables the user proceeds as follows:
To convert a quantity expressed in a unit in the left-hand column to the equivalent
in a unit in the top row of a subtable, multiply the quantity by the factor common
to both units. For example, to convert 7 ft to the equivalent in meters, go to sub-table
A, "Units of Length," and find 1 ft in the left-hand column and m in the top row.
The conversion factor common to these units is 0.3048. Therefore, 7 ft = 7 × 0.3048
= 2.1336 m.
The conversion factors have been carried out to seven significant figures, as derived
from the fundamental constants and the definitions of the units. However, this does
not mean that the factors are always known to that accuracy. Numbers followed by
ellipses are to be continued indefinitely with repetition of the same pattern of
digits. Factors written with fewer than seven significant digits are exact values.
Numbers followed by an asterisk are definitions of the relation between the two
units.
Units of temperature in measurement systems
Temperature is a basic physical quantity. It is a measure of the thermal energy
of random motion of particles in a system. As such it has been chosen as one of
the base quantities in the SI. It is to be treated as are the units of length, mass,
time, electric current, and luminous intensity. In the SI the unit of length is
the meter, the unit of time the second, and so on. The question arises as to the
choice of the unit of temperature in the SI.
In the past it was customary to refer to scales of temperature, for example, the
Celsius and Fahrenheit scales. On the Celsius scale, 0 designates the freezing point
(ice point) and 100 the boiling point (steam point) of water. Corresponding numbers
on the Fahrenheit scale are 32 and 212. There are 100 units between the ice point
and steam point on the Celsius scale, and 180 units between these points in the
Fahrenheit system.
By measuring the volume changes of a gas within the 100-unit interval of the ice
point and steam point of water on the Celsius scale, it was found that a numerical
value could be assigned for a basic unit of temperature. Careful measurement of
this ice-steam interval in a gas thermometer determined that the ice point of water
should be assigned the value of 273.15 kelvins. The unit of temperature was thus
called the kelvin with the symbol K. Further experiments led to the decision to
define the kelvin in the SI along the same lines but in terms of the triple point
of water. This is the temperature and pressure at which ice, liquid water, and water
vapor coexist at equilibrium. The triple point was chosen because it was a more
reproducible value than the ice point.
This change led to the SI definition of temperature in terms of the triple point
of water, which is exactly 273.16 kelvins.
It follows that the Celsius temperature (°C) is an intermediate scale. It is useful
in defining Kelvin temperature in the SI. Celsius temperature (t) is related to
Kelvin temperature (K) as follows:
|
tice point |
=
|
0°C |
|
tsteam point |
=
|
100°C |
|
0 K |
=
|
–273.15°C |
A summary of the conventions in the SI as proposed in the Thirteenth General Conference
of Weights and Measures pertaining to temperature units is given below.
1. The unit of SI temperature is the kelvin, symbol K.
2. The word "scale" is not to be used except in terms of measurement of temperature
between certain fixed points on the Celsius scale.
3. The terms "thermodynamic scale" or "absolute scale" are not to be used to describe
temperature. The degree sign is to be eliminated with the symbol K.
4. When Celsius temperatures are used (°C), it is understood that the temperature
unit is the kelvin.
Not all scientists and engineers have adopted the SI of temperature terminology.
For this reason the contributors to the Encyclopedia have retained the term "scale"
in relation to thermodynamic temperature. Furthermore, many engineers in the United
States still use the Fahrenheit system in discussing practical engineering systems.
In converting Fahrenheit (°F) to Celsius (°C) the following formula applies.
In converting Celsius to Fahrenheit the following formula can be used.
°F = (°C x 1.8) + 32°
In changing from Celsius terminology (t) to kelvin units (K) the following formula
can be used.
K = t + 273.15
Symbols for the chemical elements
The mass number, atomic number, number of atoms, and ionic charge of an element
are indicated by means of four indices placed around the symbol. The positions occupied
are left upper index, mass number; left lower index, atomic number; right upper
index, ionic charge; and right lower index, number of atoms of an element in a molecule
or formula unit of a given species; for example, 126C, Ca 2+,
0 2, and Al 2O 3. The atomic number, which is redundant,
is omitted in most cases; that is, 126C can be written as
12C.
Ionic charge is indicated by a plus or minus superscript following the symbol of
the ion; for multiple charges an arabic superscript numeral precedes the plus or
minus sign, for example, Na +, NO 3–, Ca 2+,
PO 43–.
Chemical nomenclature
The International Union of Pure and Applied Chemistry (IUPAC) has established definitive
rules for chemical nomenclature. Chemical species are identified by a systematic
name, frequently accompanied by a formula. Occasionally certain well-established
so-called common names are used.
For inorganic compounds, systematic names of compounds are formed by identifying
the constituents and their proportions in a specific order, for example, dinitrogen
oxide (N 2O). Also accepted by IUPAC is Stock's system, in which the proportions
of the constituents are indicated indirectly, and roman numerals are used to represent
the oxidation number or stoichiometric valence of an element, for example, iron(II)
chloride (FeCl 2). Complex compounds are also named according to rules
specified by IUPAC; an example is potassium oxodichloroimidophosphate, K[POCl 2(NH)].
Examples of accepted common names are diborane (B 2H 6), silane
(SiH 4), and ammonia (NH 3).
There also are definitive rules for naming organic compounds. Because of the infinite
variety of disciplines and industrial applications involving organic compounds,
the rules encompass different types of names. Sometimes a single compound can correctly
be identified by a number of names, for example, chloral hydrate is also known as
2,2,2- trichloro-1,1-ethanediol and trichloroacetaldehyde monohydrate.
Symbols in scientific writing
Throughout the Encyclopedia, symbols have been introduced in such a way that their
translation into words or phrases will require minimal effort on the part of the
reader. In most cases a symbol is defined at its first appearance in an article.
For example:
"The energy E in a quantum of radiation of frequency
(where the frequency is equal to the velocity of the radiation in a given medium
divided by its wavelength in the same medium) is directly proportional to the frequency,
or inversely proportional to the wavelength, according to the relation given in
Eq. (6),
|
E = h |
(6) |
where h is a universal constant known as Planck's constant. The value of
h is 6.63 × 10 -34 joule-second, and if
is expressed in s –1, E is given in joules per quantum."
For convenience, symbols commonly encountered in scientific writing are listed
here. Symbols following the ellipses and separated by commas are alternatives
that are used only when there is some reason for not using the symbol given first.
Some frequently encountered symbols for particles and quanta are as follows:
|
neutron |
n |
pion |
 |
|
proton |
p
|
muon |
µ |
|
deuteron |
d |
electron
|
e |
|
triton |
t |
neutrino |
|
|
alpha particle
|
 |
photon |
 |
The meaning of abbreviated notations for nuclear reactions should be the following:
initial nuclide (incoming particle(s) or quanta, outgoing particle(s) or quanta)
final nuclide
Some examples are:
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