Scientists and engineers have used two major systems of units and measurements, commonly referred to as the U.S. Customary System (a legacy from the British Imperial System) and the International System of Units. Technical translators, in turn, have to cope with both systems in their daily lives and may sometimes find themselves in a quandary about their correct usage.

Our objective here is to pinpoint some aspects of the International System of Units, abbreviated in all languages as SI (from Système International d’Unités).

In the U.S. Customary System, units referring to the same quantity bear an almost random relationship; e.g. a mile has 1,609 yards, a yard has 3 feet, a foot has 12 inches, and so forth. In the SI, the relationships between the units are strictly decimal (one kilometer has 1,000 meters, one meter has 1,000 millimeters, and so on).

For the sake of historical curiosity, the Decimal Metric System was created at the time of the French Revolution. Subsequently, on June 22, 1799, two platinum standards representing the meter and the kilogram were deposited in the Archives de la République in Paris. This was considered the first step in the development of the present International System of Units.

Since this is not an engineering treatise but rather a modest attempt to highlight some of the problems often encountered by translators, our approach will be more of a visual (i.e. typographical, "spatial", if you will) nature. In fact, this is just a non-exhaustive review of some aspects of the SI which, in our opinion, should be of interest to translators. The full version of the International System of Units, whose printed form is called the SI Brochure, can be found in both English and French versions at www.bipm.fr/enus/6_Publications/si/si-brochure.html. A condensed version with comments and examples by the U.S. National Institute of Standards and Technology, called Guide for the Use of the International System of Units (SI) [NIST Special Publication 811 1995 Edition], is also available at www.nist.gov. Many examples were taken from both publications.

The Two Classes of SI Units

SI units are divided into two classes: base units and derived units. Quoting from the SI Brochure:

"From the scientific point of view, the division of SI units into these two classes is to a certain extent arbitrary, because it is not essential to the physics of the subject. Nevertheless, the CGPM [Conférence Générale des Poids et Mesures], considering the advantages of a single, practical, world-wide system of units for international relations, for teaching, and for scientific work, decided to base the International System on a choice of seven well-defined units which by convention are regarded as dimensionally independent: the meter, the kilogram, the second, the ampere, the kelvin, the mole, and the candela. These SI units are called base units.

The second class of SI units is that of derived units. These are units that are formed as products of powers of the base units according to the algebraic relations linking the quantities concerned. The names and symbols of some units thus formed may be replaced by special names and symbols that can themselves be used to form expressions and symbols for other derived units. The SI units of these two classes form a coherent set of units, where coherent is used in the specialist sense of a system whose units are mutually related by rules of multiplication and division with no numerical factor other than 1. Following CIPM [Comité International des Poids et Mesures] Recommendation 1 (1969; PV, 37, 30-31 and Metrologia, 1970, 6, 66), the units of this coherent set of units are designated by the name SI units."

Please do not get discouraged by the verboseness of the paragraphs above; they were included just as a "formal icebreaker" for our discussion.

Table 1. SI base units

Due to their widespread use among scientists, a number of units are still permitted in conjunction with SI units. For example, gauss, barn, curie and the electron volt. However, their usage might be phased out.

Table 2. Examples of SI derived units expressed in terms of SI base units

SI derived units with special names and symbols

Certain SI derived units have special names and symbols; these are given in Table 3, which also includes the radian and steradian, the two so-called supplementary units.

Table 3. SI derived units with special names and symbols, including the radian and steradian

The main purpose of our having included most of these nasty little lists is to get the novice translator acquainted with the names of some units which may not be in his or her "daily menu".

Decimal multiples and submultiples of SI units

For wannabe translators —and even interpreters— not to be caught off guard, here is a list of some increasingly common prefixes used as (sub)multiples of SI units which deserve due respect, since they keep cropping up in current texts and conferences:

Table 4. SI prefixes

Please note that only the symbols for the prefixes greater than 106 are capitalized (shown in bold on Table 4), which means that one should never write such things as KW (for kilowatts), Km (for kilometer), but rather kW, km, and so on. As to the capitalization of kW, refer to Details to be Observed on page 4.

For historical reasons, the unit of mass (kilogram) is the only base unit whose name contains a prefix. Names and symbols for decimal multiples and submultiples of the unit of mass are formed by attaching prefix names to the unit name "gram" and prefix symbols to the unit symbol "g".

Example: 10^-6 kg = 1 mg (1 milligram) but not 1 µkg (1 microkilogram).

Alternative definitions for the SI prefixes and their symbols are not allowed. Therefore, in spite of their widespread use, particularly in computer jargon, it is unacceptable to use kilo (k) to represent
210 = 1024, mega (M) to represent 220 = 1 048 576, and so on. Hence, one kbyte should theoretically represent 1000 bytes, which is NOT what the whole computer industry uses. Tough luck!

Table 5. Units accepted for use with the SI

* The alternative symbol for the liter, L, was adopted by the CGPM in order to avoid the risk of confusion between the letter l and the number 1. Thus, although both l and L are internationally accepted symbols for the liter, to avoid this risk the symbol to be used in the United States is L. The script letter l is not an approved symbol for the liter.

** In the United States and some English-speaking countries, it is referred to as the "metric ton".

OK, enough of tables and numbers. From now on we will try to concentrate on the aspects that matter most for translators: how to write them accurately.

Units not accepted for use with the SI

Just for the record, the following CGS units (with their symbols) are not accepted as SI units (italicized for clarity reasons): erg (erg); dyne (dyn); poise (P); stokes (St); gauss (Gs); oersted (Oe); maxwell (Mx); stilb (sb); phot (ph); fermi (fermi); metric carat (metric carat); torr (Torr); standard atmosphere (atm); kilogram-force (kgf); micron (m); calorie (calth) (thermochemical); x unit (xu); stere (st); gamma (g); gamma (mass) (g); lambda (volume) (l). The fact that they are not accepted does not mean they are not found. It means one should try not to use them in scientific or technical papers.

DETAILS TO BE OBSERVED

Typeface

Unit symbols are printed in roman (upright) type regardless of the type used in the surrounding text, and are attached to unit symbols without a space between the prefix symbol and the unit symbol. This last rule also applies to prefixes attached to unit names.

Examples: mL (milliliter), pm (picometer), GW (gigaohm), THz (terahertz).

Thus, assuming a whole sentence is italicized, one should write "We must add only 20 mL to the blank sample". Note that "mL" is not in italics.

Capitalization

Unit symbols are printed in lower-case letters except that:

(a) the symbol or the first letter of the symbol is an uppercase letter when the name of the unit is derived from the name of a person; and

(b) the recommended symbol for the liter is L [see Table 5, footnote].

Examples: m (meter), s (second), V (volt), Pa (pascal), lm (lumen), Wb (weber)

Please compare the particular use of capitals in the names of units and in their symbols:

10 watts = 10 W, 1 kelvin = 1 K, 1 decibel = 1 dB, 1 millivolt = 1 mV

Plurals

Unit symbols do not change in the plural.

Example: l = 24 cm but not: l = 24 cms

Note: l is the quantity symbol for length.

Punctuation

Unit symbols are not followed by a period unless at the end of a sentence.

Example: "Its length is 75 cm." or "It is 75 cm long." but not: "It is 75 cm. long."

Unit symbols obtained by multiplication

Half-high (that is, vertically centered) dots or spaces are used to express a derived unit formed from two or more other units by multiplication.

Example: N . m or N m

The half-high dot or space can be imperative. For example, m " s-1 is the symbol for the meter per second (velocity) while ms-1 is the symbol for the reciprocal millisecond (103 s-1).

Percent, %

When using the % symbol, leave a space between the % symbol and the number by which it is multiplied. Further, the symbol % should be used, not the name "percent."

Example: x = 0.0025 = 0.25 % but not: x = 0.0025 = 0.25% or x = 0.25 percent

Separation of groups of numbers

In numbers, the comma (French practice) or the dot (British practice) is used only to separate the integral part of numbers from the decimal part. Numbers may be divided in groups of three in order to facilitate reading; in the SI, neither dots nor commas are ever inserted in the spaces between groups.

Examples: 76 483 522 but not: 76,483,522

43 279.168 29 but not: 43,279.168 29

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.

Space between numerical value and unit symbol

In the expression for the value of a quantity, the unit symbol is placed after the numerical value and a space is left between the numerical value and the unit symbol.

The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle: °, ', and ", respectively (see Table 6), in which case no space is left between the numerical value and the unit symbol.

Example: a = 30°22'8"

This rule means that the symbol °C for the degree Celsius is preceded by a space when one expresses the values of Celsius temperatures.

Example: t = 30.2 °C but not: t = 30.2°C or t =30.2° C.

Please note that thermodynamic temperatures in kelvins are not written with the degree symbol (°).

Example: t = 45 K but not: t = 45 °K

Observe the use in the SI Brochure (our italicization): "A difference or interval of temperature may be expressed in kelvins or in degrees Celsius". Thus, we say "degrees Celsius" but "kelvins" (and not "degrees Kelvin").

Incidentally, to indicate a temperature interval or difference, rather than a temperature, the word "degree" in full, or the abbreviation "deg", must be used. Thus, one should use "to increase the temperature by 20 degrees Celsius", and not "... by 20 °C".

Even when the value of a quantity is used in an adjectival sense, a space is left between the numerical value and the unit symbol. (This rule recognizes that unit symbols are not like ordinary words or abbreviations but are mathematical entities, and that the value of a quantity should be expressed in a way that is as independent of language as possible.)

Examples: a 100 cm tape measure but not: a 100-cm tape measure

a 10 kV resistor but not: a 10-kV resistor

Note: When unit names are spelled out, the normal rules of English apply. Thus, for example, "a roll of 10-millimeter tape" is acceptable.

Avoid the ambiguity in "pieces were laid on 15 cm boards" by rearranging the words as follows: "pieces were laid on boards 15 cm long".

Micron and Micrometer

The word "micron" should no longer be used to denote "micrometer" (m m).

Hour, Degree, Liter, and the Like

These units are not part of the SI, but are essential and used so widely that they are accepted by the CIPM for use with the SI. Sometimes we even have to use other time-related units. In particular, circumstances may require that intervals of time be expressed in weeks, months, or years. In such cases, if a standardized symbol for the unit is not available, the name of the unit should be written out in full.

Unacceptability of abbreviations for units

Because acceptable units generally have internationally recognized symbols and names, it is not permissible to use abbreviations for their unit symbols or names, such as sec (for either s or second), sq. mm (for either mm2 or square millimeter), cc (for either cm3 or cubic centimeter), mins (for either min or minutes), hrs or hr (for either h or hours), lit (for either L or liter), amps (for either A or amperes), or mps (for either m/s or meter per second).

Prefixes are also inseparable from the unit names to which they are attached. Thus, for example, millimeter, micropascal, and meganewton are single words.

Unacceptability of compound prefixes

Compound prefix symbols, that is, prefix symbols formed by the juxtaposition of two or more prefix symbols, are not permitted. This rule also applies to compound prefixes.

Example: nm (nanometer) but not: mmm (millimicrometer)

Number of units per value of a quantity

The value of a quantity is expressed using no more than one unit.

Example: l = 10.234 m but not: l =10 m 23 cm 4 mm

Note: Expressing the values of time intervals and of plane angles are exceptions to this rule. However, according to ISO 31, it is preferable to divide the degree decimally. Thus one should write 22.50° rather than 22°30’ (since 0.5° = 30’), except in fields such as cartography and astronomy.

Clarity in writing values of quantities

It must be made clear to which unit symbol a numerical value belongs and which mathematical operation applies to the value of a quantity. Also, the Guide strongly recommends that the word "to" be used to indicate a range of values for a quantity instead of a range dash (that is, a long hyphen) because the dash could be misinterpreted as a minus sign. The first of these recommendations once again recognizes that unit symbols are not like ordinary words or abbreviations but are mathematical entities.

Examples:

35 cm x 48 cm but not: 35 x 48 cm

1 MHz to 10 MHz or (1 to 10) MHz but not: 1 MHz – 10 MHz or 1 to 10 MHz

20 °C to 30 °C or (20 to 30) °C but not: 20 °C – 30 °C or 20 to 30 °C

123 g + 2 g or (123 + 2) g but not: 123 + 2 g

70 % + 5 % or (70 + 5) % but not: 70 + 5 %

240 x (1 + 10 %) V but not: 240 V + 10 % (one cannot add 240 V and 10 %)

Unacceptability of stand-alone unit symbols

Symbols for units are never used without numerical values or quantity symbols (they are not abbreviations).

Examples:

There are 106 mm in 1 km but not: there are many mm in a km

It is sold by the cubic meter but not: it is sold by the m³.

ppm, ppb, and ppt

According to the Guide, although the SI Brochure does not mention it, language-dependent terms, such as part per million, part per billion and part per trillion, and their respective abbreviations "ppm", "ppb", and "ppt" (and similar terms and abbreviations), are not acceptable for use with the SI to express the values of quantities. Forms such as those given in the following examples should be used instead:

Examples:

a stability of 0.5 (mA/A)/min but not: a stability of 0.5 ppm/min

a shift of 1.1 nm/m but not: a shift of 1.1 ppb

a sensitivity of 2 ng/kg but not: a sensitivity of 2 ppt

Because the names of numbers 109 and larger are not uniform worldwide, it is best that they be avoided entirely (in many countries, 1 billion = 1 x 1012, not 1 x 109 as in Brazil, the United States and elsewhere). The preferred way of expressing large numbers is to use powers of 10. This ambiguity in the names of numbers is one of the reasons why the use of ppm, ppb, ppt, and the like is discouraged. Another more important reason is the inappropriateness of using abbreviations that are language dependent together with internationally recognized signs and symbols, such as MPa, ln, 1013, and %, to express the values of quantities and in equations or other mathematical expressions.

Of course there are certain cases in which the use of ppm, ppb, and the like may be required by a law or a regulation, and then one has to follow such superseding regulations.

Conclusion

This list, although far from complete, tried to highlight some points to make our texts and translations as readable and clear as possible. In our opinion, translators who want to do a professional job (or at least help their clients do it) should keep these guidelines in mind. Have fun (and accuracy)!