10 More on Printing and Using Symbols and Numbers in Scientific and
Technical Documents
By following the guidance given in this chapter
(footnote 6), NIST authors can prepare
manuscripts that are consistent with accepted typesetting practice.
10.1 Kinds of symbols
Letter symbols are of three principal kinds: (a) symbols for quantities,
(b) symbols for units, and (c) symbols for descriptive terms.
Quantity symbols, which are always printed in italic (that is, sloping) type,
are, with few exceptions, single letters of the Latin or Greek alphabets which
may have subscripts or superscripts or other identifying signs. Symbols for
units, in particular those for acceptable units, have been discussed in detail
in earlier portions of this Guide. Symbols for descriptive terms include
the symbols for the chemical elements, certain mathematical symbols, and
modifying superscripts and subscripts on quantity symbols.
10.1.1 Standardized quantity symbols
The use of words, acronyms, or other ad hoc groups of letters as
quantity symbols should be avoided by NIST authors. For example, use the
quantity symbol Zm for mechanical impedance, not MI.
In fact, there are nationally and internationally accepted symbols for
literally hundreds of quantities used in the physical sciences and technology.
Many of these are given in Refs. [6] and
[7], and it is likely that symbols for the
quantities used in most NIST publications can be found in these international
standards or can readily be adapted from the symbols and principles given in
these standards. Because of their international acceptance, NIST authors are
urged to use the symbols of Refs. [6] and [7] to the fullest extent
possible. (Footnote 7)
Examples: |
|
(solid angle) |
Zm |
(mechanical impedance) |
LP |
(level of a power quantity) |
r |
(relative mass excess) |
p |
(pressure) |
tot |
(total cross-section) |
T |
(isothermal compressibility) |
Eu |
(Euler number) |
E |
(electric field strength) |
TN |
(Néel temperature) |
10.1.2 Standardized mathematical signs and symbols
As is the case for quantity symbols, most of the mathematical signs and symbols
used in the physical sciences and technology are standardized. They may be
found in Ref. [6: ISO 31-11] and
should be used by NIST authors to the fullest possible extent.
(Footnote 7)
Examples: |
^ |
(conjunction sign,
p ^ q means p and q) |
|
(a b,
a is not equal to b) |
|
(a b, a is by definition equal to b) |
|
(a
b, a is approximately equal to b) |
~ |
(a ~ b, a is proportional to b) |
arcsin x |
(arc sine of x) |
loga x |
(logarithm to the base a of x) |
lb x |
(lb x = log2 x) |
ln x |
(ln x = loge x) |
lg x |
(lg x = log10 x) |
10.2 Typefaces for symbols
Most word processing systems now in use at NIST are capable of producing
lightface (that is, regular) or boldface letters of the Latin or Greek
alphabets in both roman (upright) and italic (sloping) types. The
understandability of NIST typed and typeset scientific and technical
publications is facilitated if symbols are in the correct typeface.
The typeface in which a symbol appears helps to define what the symbol
represents. For example, irrespective of the typeface used in the surrounding
text, "A" would be typed or typeset in
- italic type for the scalar quantity area: A;
- roman type for the unit ampere: A;
- italic boldface for the vector quantity vector potential:
A.
More specifically, the three major categories of symbols found in scientific
and technical publications should be typed or typeset in either italic or roman
type, as follows:
- symbols for quantities and variables: italic;
- symbols for units: roman;
- symbols for descriptive terms: roman.
These rules imply that a subscript or superscript on a quantity symbol is in
roman type if it is descriptive (for example, if it is a number or represents
the name of a person or a particle); but it is in italic type if it represents
a quantity, or is a variable such as x in Ex or an
index such as i in ixi that represents a
number (see Sec. 10.2.1,
Sec. 10.2.3, and
Sec. 10.2.4). An index that represents a number is
also called a "running number"
[6: ISO 31-0].
Notes: |
- 1
- The above rules also imply, for example, that µ, the symbol for
the SI prefix micro (10-6), that , the symbol for the SI derived unit ohm, and that F, the
symbol for the SI derived unit farad, are in roman type; but they are in italic
type if they represent quantities (µ, , and F are the recommended symbols for the
quantities magnetic moment of a particle, solid angle, and force, respectively).
- 2
- The typeface for numbers is discussed in
Sec. 10.5.1.
|
The following four sections give examples of the proper typefaces for these
three major categories.
10.2.1 Quantities and variables - italic
Symbols for quantities are italic, as are symbols for functions in general,
for example, f (x):
t = 3 s |
t time, s second |
T = 22 K |
T temperature, K kelvin |
r = 11 cm |
r radius, cm centimeter |
= 633 nm |
wavelength,
nm nanometer |
Constants are usually physical quantities and thus their symbols are italic;
however, in general, symbols used as subscripts and superscripts are roman if
descriptive (see Sec. 10.2.3):
NA |
Avogadro constant, A Avogadro |
R |
molar gas constant |
D |
Debye temperature, D Debye |
Z |
atomic number |
e |
elementary charge |
me |
m mass, e electron |
Running numbers and symbols for variables in mathematical equations are italic,
as are symbols for parameters such as a and b that may be
considered constant in a given context:
Symbols for vectors are boldface italic, symbols for tensors are sans-serif
bold italic, and symbols for matrices are italic:
A · B = C (vectors) |
T
(tensors) |
|
Symbols used as subscripts and superscripts are italic if they represent
quantities or variables:
cp p pressure |
qm m mass |
solid angle |
z
z coordinate |
10.2.2 Units - roman
The symbols for units and SI prefixes are roman:
m |
meter |
g |
gram |
L |
liter |
cm |
centimeter |
µg |
microgram |
mL |
milliliter |
10.2.3 Descriptive terms - roman
Symbols representing purely descriptive terms (for example, the chemical
elements) are roman, as are symbols representing mathematical constants that
never change (for example, ) and
symbols representing explicitly defined functions or well defined operators
(for example, (x) or div):
Chemical elements:
Ar argon |
B boron |
C carbon |
Mathematical constants, functions, and operators:
e |
base of natural logarithms |
xi |
|
sum of |
exp x |
exp |
exponential of |
loga x |
loga |
logarithm to the base a of |
dx/dt |
d |
1st derivative of |
sin x |
sin |
sine of |
Symbols used as subscripts and superscripts are roman if descriptive:
|
ir irrational |
Ek |
k kinetic |
|
m molar, 1 liquid phase |
µB |
B Bohr |
10.2.4 Sample equations showing correct type
|
F = ma |
pV = nRT |
|
Ea = RT2 d(ln k)/dT |
|
E = mc2 |
|
|
10.3 Greek alphabet in roman and italic type
Table 13 shows the proper form, in both roman and italic type, of the upper-case and lower-case
letters of the Greek alphabet.
Table 13. Greek alphabet in roman and italic type
Name |
Capital Roman |
Lower Case Roman |
Capital Italic |
Lower Case Italic |
|
alpha |
A |
|
A |
|
beta |
B |
|
B |
|
gamma |
|
|
|
|
delta |
|
|
|
|
epsilon |
E |
,
|
E |
,
|
zeta |
Z |
|
Z |
|
eta |
H |
|
H |
|
theta |
,
(a) |
,
(b) |
,
(a) |
,
(b) |
iota |
I |
|
I |
|
kappa |
K |
,
(b) |
K |
,
(b) |
lambda |
|
|
|
|
mu |
M |
µ |
M |
µ |
nu |
N |
|
N |
|
xi |
|
|
|
|
omicron |
O |
o |
O |
o |
pi |
|
,
|
|
,
|
rho |
P |
,
(b) |
P |
,
(b) |
sigma |
|
|
|
|
tau |
T |
|
T |
|
upsilon |
|
|
|
|
phi |
|
,
|
|
,
|
chi |
X |
|
X |
|
psi |
|
|
|
|
omega |
|
|
|
|
|
(a) ISO (see Ref. [6: ISO 31-0])
gives only the first of these two letters.
(b) ISO (see Ref. [6: ISO 31-0])
gives these two letters in the reverse order. |
10.4 Symbols for the elements
The following two sections give the rules and style conventions for the symbols
for the elements.
10.4.1 Typeface and punctuation for element symbols
Symbols for the elements are normally printed in roman type without regard to
the type used in the surrounding text (see
Sec. 10.2.3). They are not followed by a period
unless at the end of a sentence.
10.4.2 Subscripts and superscripts on element symbols
The nucleon number (mass number) of a nuclide is indicated in the left
superscript position: 28Si.
The number of atoms in a molecule of a particular nuclide is shown in the right
subscript position: 1H2.
The proton number (atomic number) is indicated in the left subscript position:
29Cu.
The state of ionization or excitation is indicated in the right superscript
position, some examples of which are as follows:
State of ionization: |
Ba++ |
or
or |
Electronic excited state: |
Ne*, CO* |
Nuclear excited state: |
15N* or 15Nm |
10.5 Printing numbers
The following three sections give rules and style conventions related to the
printing of numbers.
10.5.1 Typeface for numbers
Arabic numerals expressing the numerical values of quantities (see
Sec. 7.6) are generally printed in lightface
(that is, regular) roman type irrespective of the type used for the surrounding
text. Arabic numerals other than numerical values of quantities may be printed
in lightface or bold italics, or in bold roman type, but lightface roman type
is usually preferred.
10.5.2 Decimal sign or marker
The recommended decimal sign or marker for use in the United States is the dot
on the line [4, 8].
For numbers less than one, a zero is written before the decimal marker. For
example, 0.25 s is the correct form, not .25 s.
10.5.3 Grouping digits
Because the comma is widely used as the decimal marker outside the United
States, it should not be used to separate digits into groups of three. Instead,
digits should be separated into groups of three, counting from the decimal
marker towards the left and right, by the use of a thin, fixed space.
However, this practice is not usually followed for numbers having only four
digits on either side of the decimal marker except when uniformity in a table
is desired.
Examples: |
76 483 522 |
but not: |
76,483,522 |
43 279.168 29 |
but not: |
43,279.168 29 |
8012 or 8 012 |
but not: |
8,012 |
0.491 722 3 |
is highly preferred to: |
0.4917223 |
0.5947 or 0.594 7 |
but not: |
0.59 47 |
8012.5947 or 8 012.594 7 |
but not: |
8 012.5947 or 8012.594 7
|
Note: |
The practice of using a space to group digits is not usually
followed in certain specialized applications, such as engineering drawings and
financial statements. |
10.5.4 Multiplying numbers
When the dot is used as the decimal marker as in the United States, the
preferred sign for the multiplication of numbers or values of quantities is a
cross (that is, multiplication sign) ( x ), not a half-high (that
is, centered) dot ( · ).
Examples: |
25 x 60.5 |
but not: |
25 · 60.5 |
53 m/s x 10.2 s |
but not: |
53 m/s · 10.2 s |
15 x 72 kg |
but not: |
15 · 72 kg
|
Notes: |
- 1
- When the comma is used as the decimal marker, the preferred sign for
the multiplication of numbers is the half-high dot. However, even when the
comma is so used, this Guide prefers the cross for the multiplication of
values of quantities.
- 2
- The multiplication of quantity symbols (or numbers in parentheses or
values of quantities in parentheses) may be indicated in one of the following
ways: ab, a b, a · b,
a x b.
|