GUIDE OR METRIC PRACTICE Internationally recognized conventions have been established for standard usage of SI units. Robert A. Nelson ROBERT NELSON is the author of the booklet SI: The International System of Units, 2nd ed. (American Association of Physics Teachers, College Park, Maryland, 1982). He is president of Satellite Engineering Research Corporation, a consulting firm in Bethesda, Maryland, and teaches in the department of aerospace engineering at the University of Maryland. he modernized metric system is known as the Système TInternational d’Unités (International System of Table 1. SI base units Units), with the international abbreviation SI. It is found- Quantity Unit ed on seven base units, listed in table 1, that by conven- Name Symbol tion are regarded as dimensionally independent. All other length meter m mass kilogram kg units are derived units, formed coherently by multiplying time second s and dividing units within the system without numerical electric current ampere A factors. Examples of derived units, including some with thermodynamic temperature kelvin K special names, are listed in table 2. The expression of amount of substance mole mol multiples and submultiples of SI units is facilitated luminous intensity candela cd through the use of the prefixes listed in table 3. SI obtains its international authority from the Meter Convention, signed in Paris by the delegates of 17 coun- Table 2. Examples of SI derived units tries, including the United States, on 20 May 1875, and Quantity Unit Special name Symbol Equivalent amended in 1921. Today 49 countries are members. The plane angle radian rad m/m=1 treaty established the Conférence Générale des Poids et solid angle steradian sr m22 /m =1 speed, velocity m/s Mesures (General Conference on Weights and Measures) acceleration m/s2 as the formal diplomatic body responsible for ratification angular velocity rad/s of new proposals related to metric units. The scientific angular acceleration rad/s2 frequency hertz Hz s–1 decisions are made by the Comité International des Poids force newton N kg·m/s2 et Mesures (International Committee for Weights and pressure, stress pascal Pa N/m2 Measures). It is assisted by the advice of ten Consultative work, energy, heat joule J N·m, kg·m22 /s impulse, momentum N·s, kg·m/s Committees specializing in particular areas of metrology. power watt W J/s The activities of the national standards laboratories are electric charge coulomb C A·s coordinated by the Bureau International des Poids et electric potential, emf volt V J/C, W/A resistance ohmW V/A Mesures (International Bureau of Weights and Measures), conductance siemens S A/V, W–1 which has its headquarters in Sèvres, France, and oper- magnetic flux weber Wb V·s inductance henry H Wb/A ates under the supervision of the CIPM. The SI was estab- capacitance farad F C/V lished by the 11th CGPM in 1960, when the metric unit electric field strength V/m, N/C magnetic flux density tesla T Wb/m2 , N/(A·m) definitions, symbols, and terminology were extensively 2 1 electric displacement C/m revised and simplified. magnetic field strength A/m The BIPM, with the guidance of the Consultative Celsius temperature degree Celsius °C K luminous flux lumen lm cd·sr Committee for Units and approval of the CIPM, periodi- 2 2 illuminance lux lx lm/m cally publishes a document that summarizes the histori- radioactivity becquerel Bq s–1 cal decisions of the CGPM and the CIPM and gives some catalytic activity katal kat mol/s conventions for metric practice. In addition, Technical Committee 12 of the International Organization for Stan- Style conventions dardization has prepared recommendations concerning Letter symbols include quantity symbols and unit sym- the practical use of the SI.3 Some other recommendations bols. Symbols for physical quantities are set in italic (slop- have been given by the Commission for Symbols, Units, ing) type, while symbols for units are set in roman Nomenclature, Atomic Masses and Fundamental Con- (upright) type (for example, F = 15 N). stants of the International Union of Pure and Applied A unit symbol is a universal mathematical entity. It is Physics.4 The National Institute of Standards and Tech- not an abbreviation and is not followed by a period (for nology (NIST) has published a practical guide for the use example, the symbol for second is s, not sec or s.). Symbols of the SI.5 The Institute of Electrical and Electronics Engi- for units with proper names have the first letter capital- neers (IEEE) and the American Society for Testing and ized—otherwise unit symbols are lower case—but the unit Materials (ASTM) have jointly prepared a metric practice names themselves are not capitalized (for example, tesla, manual6 that has been recognized by the American Nation- T; meter, m). In contrast to unit symbols, the spelling and al Standards Institute (ANSI). The Secretary of Commerce, grammar for unit names are specific to a given language through NIST, has also issued recommendations for US and are not part of the SI (for example, the spellings kilo- metric practice,7 as provided under the Metric Conversion gram and ampere are used in English, while kilogramme Act of 1975 and the Omnibus Trade and Competitiveness and ampère are used in French, but kg and A are the uni- Act of 1988. Additional information is available on the versal SI symbols). Plurals of unit names are formed Internet at the BIPM8 and NIST9 Web sites. according to the usual rules of grammar (for example, AUGUST 2001 PHYSICS TODAY BG15 © 2001 American Institute of Physics, S-0031-9228-0182-020-2 Table 3. SI prefixes Table 5. Non-SI units accepted for use with Factor Prefix Symbol Factor Prefix Symbol the SI whose values in SI units are obtained 1024 yotta Y 10–1 deci d 1021 zetta Z 10–2 centi c experimentally 1018 exa E 10–3 milli m Quantity Unit 1015 peta P 10–6 micro m Name Symbol Value 1012 tera T 10–9 nano n energy electron volt* eV 1.602 176 462(63)× 10–19 J 109 giga G 10–12 pico p mass unified atomic u 1.660 538 73(13)× 10–27 kg 106 mega M 10–15 femto f mass unit* 3 –18 10 kilo k 10 atto a distance astronomical unit** ua 1.495 978 706 91(6)× 1011 m 102 hecto h 10–21 zepto z 101 deka da 10–24 yocto y * P. J. Mohr, B. N. Taylor,J. Phys. Chem. Ref. Data28 , 1713 (1999). Rev. Mod. Phys. 72 , 351 (2000). ** D. D. McCarthy, ed.,IERS Conventions (2000) , to be published; http://www.iers.org. Table 4. Units accepted for use with the SI Quantity Unit example, 299 792 458, not 299,792,458) to avoid confusion Name Symbol Definition with the decimal marker in European literature. This time minute min 1 min=60 s spacing convention is also used to the right of the decimal hour h 1 h=60 min=3600 s day d 1 d=24 h=86 400 s marker. The numerical value and unit symbol must be plane angle degree ° 1°=(p /180) rad separated by a space, even when used as an adjective (for minuteЈЈ 1 =(1/60)°=(p /10 800) rad example, 35 mm, not 35mm or 35-mm). A zero should be secondЉЉЈ 1 =(1/60) =(p /648 800) rad placed in front of the decimal marker in decimal fractions volume liter L 1 L=1 dm3 =10–33 m (for example, 0.3 J, not .3 J). mass metric ton t 1 t=1000 kg attenuation, level neper Np 1 Np=1 Non-SI units bel B 1 B=1 / ln 10 Np 2 An important function of the SI is to discourage the pro- liferation of unnecessary units. However, there are three kilopascals, henries) with the exceptions lux, hertz, and categories of units outside the SI that are recognized. 5 siemens, which are irregular. Unit symbols are not plu- “Units accepted for use with the SI” are listed in Table 4. ralized (for example, 3 kg, not 3 kgs). As exceptions to the rules, the symbols °, Ј and Љ for plane The word “degree” and its symbol, °, are omitted from angle are not preceded by a space, and the symbol for liter, the unit of thermodynamic temperature T (that is, one L, is capitalized to avoid confusion with the number 1. uses kelvin or K, not degree Kelvin or °K). However, they “Non-SI units accepted for use with the SI whose values are retained in the unit of Celsius temperature t, defined in SI units are obtained experimentally” are given in as t T–T , where T = 273.15 K exactly (that is, degree 0 0 Table 5. The third category, “other non-SI units currently Celsius, °C). accepted for use with the SI,” consists of the nautical mile, 6 Symbols for prefixes representing 10 or greater are knot, are, hectare, bar, angstrom, and barn. capitalized; all others are lower case. There is no space between the prefix and the unit. Compound prefixes are to References be avoided (for example, pF, not mmF). An exponent 1. For a history of the metric system and SI units, see R. A. Nel- applies to the whole unit including its prefix (for example, son, Phys. Teach. 19, 596–613 (1981); R. A. Nelson, Via Satel- cm3 = 10–6 m3). When a unit multiple or submultiple is lite 15 (2), 90–108 (2000). written out in full, the prefix should be written in full, 2. Bureau International des Poids et Mesures, Le Système Inter- beginning with a lower-case letter (for example, mega- national d'Unités (SI), 7th ed., BIPM, Sèvres, France (1998); hertz, not Megahertz or Mhertz).