The International System of Units (SI)

Understanding SI Units

Do you need to have an understanding of SI units in your line of work? I know copy editors, proofreaders, and authors of scientific manuscripts, theses, and dissertations need to. In the following, I take a closer look at the International System of Units (SI); in particular, I focus on the ways in which SI units should be typeset in strict accordance with the SI guidelines.

I note here that many publications do not observe certain SI conventions regarding the typesetting of SI units — a prime example being the SI stipulation that a space should precede the percent sign (%) and the symbol for degrees of temperature (°C).


The information below has been adapted from the following sources:


The International System of Units (SI) consists of a set of base units, a set of derived units, and a set of prefixes.

SI Units

The base units are the building blocks of the system, and all other units are derived from them.

The derived units are unlimited in number, and some have special names and symbols.

Prefix names/symbols are added to unit names/symbols to produce multiples and submultiples of the original units. For example, consider the following:

  • prefix name “milli” is added to unit name “metre” to form “millimetre
  • prefix symbol “m” is added to unit symbol “m” to form “mm

Understanding SI Units

  • Names of Units

  • Expressing Values of Quantities

  • Unit Symbols

  • Prefixes

  • Numbers


Names of Units

The writing of unit names and of their plural forms is language-specific. 

  • British English uses the spelling deca-, metre, and litre
  • American English uses the spelling deka-, meter, and liter
  • Regular plural: “henry” becomes “henries
  • Irregular plurals: lux, hertz, and siemens remain the same in both their singular and plural form

Names of units follow the grammatical rules associated with common nouns: in English and in French they start with a lowercase letter (e.g., newton, hertz, pascal), even when the symbol for the unit begins with a capital letter.

In English, when unit names are combined to denote multiplication of the units concerned, they are separated with a hyphen or a space.

  • newtonmetre or newton metre

The plural is formed by converting the last unit name to the plural form.

  • ten newtonmetres

It is not permissible to use abbreviations for unit symbols or unit names. 

  • It is not permissible to write “sec” for either s or second 
  • It is not permissible to write “sq. mm” for either mm² or square millimetre
  • It is not permissible to write “cc” for either cm³ or cubic centimetre
  • It is not permissible to write “mps” for either m/s or metre per second

When the name of a derived unit is formed from the names of individual units by multiplication, then either a space or a hyphen is used to separate the names of the individual units.

  • pascal second or pascalsecond.

In English, modifiers such as “squared” or “cubed” are used in the names of units raised to powers, and they are placed after the unit name

  • metre per second squared

However, in the case of area and volume, where the modifiers “square” and “cubic” may be used, respectively, such modifiers are placed before the unit name

  • square centimetre
  • cubic centimetre
  • ampere per square metre
  • kilogram per cubic metre

Unit names as adjectives: A space between the number and the unit symbol is specified when the combination is used as an adjective.

  • “a 25 kg sphere” 

However, in English, a hyphen would be used as normal in this context if the unit name is spelt out.

  • “a 25kilogram sphere”

Understanding SI Units

  • Names of Units

  • Expressing Values of Quantities

  • Unit Symbols

  • Prefixes

  • Numbers


Expressing Values of Quantities

The underlying principle behind all SI units is as follows:

value of a quantity = number × unit

The value of a quantity is written as a number followed by a space — representing a multiplication sign — and a unit symbol.

  • 2.21 kg
  • 7.3 × 102 m2
  • 22 K

This rule explicitly includes the percent sign (%) and the symbol for degrees of temperature (°C) — exceptions are the symbols for plane angular degrees, minutes, and seconds (°, ′, and ″), which are placed immediately after the number with no intervening space.

  • Acceptable: 56 %
  • Acceptable: 24 °C
  • Not acceptable: 67%
  • Not acceptable: 39°C

Understanding SI Units

  • Names of Units

  • Expressing Values of Quantities

  • Unit Symbols

  • Prefixes

  • Numbers


Unit Symbols

Symbols are mathematical entities, not abbreviations, and as such do not have an appended period/full stop (.), unless the rules of grammar demand one for another reason, such as denoting the end of a sentence.

Symbols for derived units formed by multiplication are joined with a centre dot (·) or a non-breaking space

  • N·m or N m

Symbols for derived units formed by division are joined with a solidus (/), or given as a negative exponent.

  • “metre per second” can be written m/s, m s−1, m·s−1

Only one solidus should be used.

  • Acceptable: kg/(m·s2) and kg·m−1·s−2
  • Not acceptable: kg/m/s2

The first letter of unit symbols derived from the name of a person is written in upper case; otherwise, they are written in lower case.

  • The unit of pressure is named after Blaise Pascal, so its corresponding unit symbol is written “Pa”.
  • The litre may exceptionally be written using either an uppercase “L” or a lowercase “l”; the American NIST recommends that within the United States “L” be used rather than “l”.

Symbols of units do not have a plural form.

  • Acceptable: 25 kg (plural)
  • Not acceptable: 25 kgs

Symbols are written in upright (Roman) type (m for metres, s for seconds), so as to differentiate from the italic type used for quantities (m for mass, s for displacement). By consensus of international standards bodies, this rule is applied independent of the font used for surrounding text.


Understanding SI Units

  • Names of Units

  • Expressing Values of Quantities

  • Unit Symbols

  • Prefixes

  • Numbers


Prefixes

A prefix is part of the unit, and its symbol is prepended to the unit symbol without a separator.

  • k in km
  • M in MPa
  • G in GHz

Compound prefixes are not allowed.


Understanding SI Units

  • Names of Units

  • Expressing Values of Quantities

  • Unit Symbols

  • Prefixes

  • Numbers


Numbers

The 10th resolution of CGPM in 2003 declared that “the symbol for the decimal marker shall be either the point on the line or the comma on the line.” In practice, the decimal point is used in English-speaking countries and most of Asia, and the comma in most of Latin America and in continental European countries.

  • Acceptable: 0.123
  • Acceptable: 0,123

If the number is between +1 and −1, then the decimal marker is always preceded by a zero.

  • Acceptable: 0.123
  • Acceptable: 0.7
  • Not acceptable: .123
  • Not acceptable .7

Thin spaces should be used as a thousands separator.

  • Acceptable: 1 000 000
  • Not acceptable: 1,000,000
  • Not acceptable: 1.000.000

However, when there are only four digits before or after the decimal marker, it is customary not to use a thin space to isolate a single digit. The practice of grouping digits in this way is a matter of choice; it is not always followed in certain specialized applications such as engineering drawings, financial statements, and scripts to be read by a computer.

Any line-break inside a number, inside a compound unit, or between number and unit should be avoided. Where this is not possible, line breaks should coincide with thousands separators.

Since the value of “billion” and “trillion” can vary from language to language, the dimensionless terms “ppb” (parts per billion) and “ppt” (parts per trillion) should be avoided. No alternative is suggested in the SI Brochure.


Robert Astle is a copy editor of scientific manuscripts, theses, and dissertations written by ESL authors. He specializes in the fields of information, telecommunications, electronics, and mathematics.

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