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40334 Federal Register / Vol. 63, No. 144 / Tuesday, July 28, 1998 / Notices

DEPARTMENT OF COMMERCE weights and measures for United States SI prefixes to form decimal multiples trade and commerce; and submultiples of SI units; and (2) the National Institute of Standards and ‘‘(2) to require that each Federal elimination of the class of Technology agency, by a date certain and to the supplementary units (the and the extent economically feasible by the end [Docket No. 980430113±8113±01] ) as a separate class in the SI. of the fiscal year 1992, use the metric Further, the International Committee for Metric : system of measurement in its Weights and Measures (abbreviated Interpretation of the International procurements, grants, and other CIPM after the French Comite´ System of Units for the United States business related activities, except to the International des Poids et Mesures), extent that such use is impractical or is which comes under the authority of the AGENCY: National Institute of Standards likely to cause significant inefficiencies CGPM, has made some new and Technology, Commerce. or loss of markets to United States firms, recommendations regarding units not ACTION: Notice. such as when foreign competitors are part of the SI that may be used with the producing competing products in non- SI. It is therefore necessary to issue new SUMMARY: This notice restates the metric units; tables and associated text that reflect interpretation of the International ‘‘(3) to seek out ways to increase these changes and which set forth a new System of Units (SI) for the United understanding of the metric system of interpretation of the SI for the United States by the Department of Commerce. measurement through educational States. Thus this Federal Register notice This interpretation was last published information and guidance and in supersedes the previous interpretation by the Department of Commerce in the Government publications; and Federal Register on December 20, 1990 ‘‘(4) to permit the continued use of published in the Federal Register on (55 FR 52242–52245). Since the traditional systems of weights and December 20, 1990 (55 FR 52242– publication of that notice, the measures in nonbusiness activities.’’ 52245). international bodies that are responsible In the Metric Conversion Act of 1975, Classes of SI Units for the SI have made some changes to the ‘‘metric system of measurement’’ is it. It has therefore become necessary to defined as the International System of There are now only two classes of set forth a new interpretation of the SI Units as established in 1960 by the units in the International System of for the United States that reflects these General Conference of Weights and Units: base units and derived units. The changes. Measures (abbreviated CGPM after the units of these two classes form a FOR FURTHER INFORMATION CONTACT: For French Confe´rence Ge´ne´ral des Poids et coherent set of units and are designated information regarding the International Mesures) and interpreted or modified by the name ‘‘SI units.’’ Here, the term System of Units, contact Dr. Barry N. for the United States by the Secretary of coherent is used to mean a unit system Taylor, Building 225, Room B161, Commerce (15 U.S.C. 205c). The where all derived units are obtained National Institute of Standards and Secretary has delegated this authority to from the base units by the rules of Technology, Gaithersburg, MD 20899– the Director of the National Institute of multiplication and division with no 0001, telephone number (301) 975– Standards and Technology. In numerical factor other than the number 4220. For information regarding the implementation of this authority, tables 1 ever occurring in the expressions for Federal Government’s efforts to and associated text were published in the derived units in terms of the base coordinate the transition of the United the Federal Register of December 20, units. The SI also includes prefixes to States to the International System of 1990 (55 FR 52242–52245), setting forth form decimal multiples and Units, contact Mr. James B. McCracken, the interpretation for the United States submultiples of SI units. Because units Metric Program, Building 820, Room of the International System of Units formed with SI prefixes are not coherent 306, National Institute of Standards and (abbreviated SI in all languages after the with SI units, the units so formed are Technology, Gaithersburg, MD 20899– French Syste´me International d’Unite´s). designated by their complete name 0001, telephone number (301) 975– The CGPM is an intergovernmental ‘‘decimal multiples and submultiples of 3690, email: [email protected] organization established by the Meter SI units’’ in order to make a distinction SUPPLEMENTARY INFORMATION: Section Convention (Convention du Me´tre), between them and the coherent set of SI 5164 of Public Law 100–418, the which was signed by the United States units proper. The SI units and their Omnibus Trade and Competitiveness and 16 other countries in Paris in 1875 decimal multiples and submultiples Act of 1988, amended Public Law 94– (nearly 50 countries are now members together are often called ‘‘units of the 168, the Metric Conversion Act of 1975. of the Convention). One of the In particular, section 3 of the Metric responsibilities of the CGPM is to SI.’’ Conversion Act (codified as amended 15 ensure that the SI reflects the latest SI Base Units U.S.C. 205b) reads as follows: advances in science and technology. ‘‘Sec. 3. It is therefore the declared Since the publication of the 1990 The SI is founded on seven SI base policy of the United States— Federal Register notice, the CGPM has units for seven base quantities assumed ‘‘(1) to designate the metric system of made two significant changes to the SI. to be mutually independent. These units measurement as the preferred system of These are (1) the addition of four new and quantities are given in Table 1. Federal Register / Vol. 63, No. 144 / Tuesday, July 28, 1998 / Notices 40335

SI Derived Units for these derived quantities are obtained products of powers (both positive and from this system of equations and the negative) of the SI base units Other quantities, called derived seven SI base units in a coherent corresponding to the base quantities quantities, are defined in terms of these manner, which means, in keeping with concerned without numerical factors. seven base quantities through a system the above discussion of the term Table 2 gives some examples of SI of quantity equations. SI derived units coherent, that they are formed as derived units.

Quantities of Dimension 1 expressed by the number 1, are relative 3 and are discussed in connection with The last entry of Table 2, mass permeability, dynamic friction factor, Table 4, are two such examples. refractive index, characteristic numbers fraction, is an example of certain SI Derived Units With Special Names such as the Mach number, and numbers derived quantities that are defined as and Symbols the ratio of two mutually comparable that represent a count, such as a number quantities, that is, two quantities of the of molecules. However, the number 1 is For ease of understanding and same kind. Since the coherent SI generally not explicitly shown in the convenience, 21 SI derived units have derived unit of such a derived quantity expression for the value of a quantity of been given special names and symbols. is the ratio of two identical SI units, that dimension 1. For example, the value of These are listed in Table 3, where it unit may also be expressed by the the refractive index of a given medium should be noted that the last three units number one, symbol 1. Such quantities is expressed as n = 1.51 rather than as of Table 3, the , unit symbol are called quantities of dimension 1, or n = 1.51 × 1. In a few cases a special Bq, the , unit symbol Gy, and the dimensionless quantities, and the SI name and symbol are given to the , unit symbol Sv, were unit of all such quantities is the number number 1 to aid understanding. The specifically introduced by the CGPM 1. Examples of other derived quantities radian, unit symbol rad, and steradian, with a view to safeguarding human of dimension 1, and thus with a unit symbol sr, which are given in Table coherent SI derived unit that may be health. 40336 Federal Register / Vol. 63, No. 144 / Tuesday, July 28, 1998 / Notices

Degree t T and the triple point of water may be = − 27315.. ∆ ° ∆ °CK written as t = 29.7546 C = T = The derived unit in Table 3 with 29.7546 K. (Note that the centigrade special name Celsius and special It follows from the definition of t that temperature scale is obsolete; the unit ° symbol C deserves comment. Because the degree Celsius is equal in magnitude name degree centigrade should no of the way temperature scales used to be to the , which in turn implies that longer be used.) defined, it remains common practice to the numerical value of a given express a thermodynamic temperature, temperature difference or temperature Use of SI Derived Units With Special symbol T, in terms of its difference from interval whose value is expressed in the Names and Symbols ° the reference temperature T0 = 273.15 K, unit degree Celsius ( C) is equal to the The special names and symbols of the the ice point. This temperature numerical value of the same difference 21 SI derived units with special names difference is called Celsius temperature, or interval when its value is expressed and symbols given in Table 3 may symbol t, and is defined by the quantity in the unit kelvin (K). Thus temperature differences or temperature intervals may themselves be included in the names equation t = T¥T0. The unit of Celsius be expressed in either the degree Celsius and symbols of other SI derived units. temperature is the degree Celsius, ° or the kelvin using the same numerical This use is shown in Table 4. All of the symbol C. The numerical value of a value. For example, the Celsius SI derived units in Table 4, like those Celsius temperature t expressed in temperature difference ∆t and the in Table 3, have been obtained from the degrees Celsius is given by thermodynamic temperature difference SI base units in the same coherent ∆T between the melting point of gallium manner discussed above. Federal Register / Vol. 63, No. 144 / Tuesday, July 28, 1998 / Notices 40337

Radian and Steradian of the same kind but are of the same to note that the is the only SI dimension (that is, derived quantities unit with a prefix as part of its name and As indicated in Table 3, the radian, whose units when expressed in SI base symbol. Because multiple prefixes may unit symbol rad, and steradian, unit units are the same). Table 4 includes not be used, in the case of the kilogram symbol sr, are the special names and some examples of derived units that use the prefix names of Table 5 are used symbols for the derived units of plane the radian and steradian. with the unit name ‘‘gram’’ and the angle and solid angle, respectively. prefix symbols are used with the unit SI Prefixes These units may be used or not in symbol ‘‘g.’’ With this exception, any SI expressions for derived units as is Table 5 gives the 20 SI prefixes used prefix may be used with any SI unit, convenient in order to distinguish to form decimal multiples and including the degree Celsius and its between derived quantities that are not submultiples of SI units. It is important symbol °C. 40338 Federal Register / Vol. 63, No. 144 / Tuesday, July 28, 1998 / Notices

Because the SI prefixes strictly Units Outside the SI with the recommendations of the CIPM, represent powers of 10, it is the units in this category that are inappropriate to use them to represent Certain units are not part of the accepted for use in the United States powers of 2. Thus 1 kbit = 103 bit = International System of Units, that is, with the SI are given in Tables 6 and 7. 1000 bit and not 210 = 1024 bit, where they are outside the SI, but are 1 kbit is one kilobit. important and widely used. Consistent

Liter and Metric Ton confusion between the letter l and the metric ton, this is the name to be used number 1. Thus, although both l and L in the United States for the unit with The units liter and metric ton in Table are internationally accepted symbols for symbol t and defined according to 1 t = 6 deserve comment. The liter and its the liter, to avoid this risk the preferred 103 kg. (The name ‘‘metric ton’’ is also symbol l were adopted by the CIPM in symbol for use in the United States is L. used in some other English speaking 1879. The alternative symbol for the Neither a lowercase script letter l nor an countries, but the name ‘‘’’ is used liter, L, was adopted by the CGPM in uppercase script letter l are approved in many countries.) 1979 in order to avoid the risk of symbols for the liter. With regard to the Federal Register / Vol. 63, No. 144 / Tuesday, July 28, 1998 / Notices 40339

Other Units Outside the SI document in which they are used; their dealing with health and safety, this Other units outside the SI that are continued use is not encouraged. The interpretation of the SI for the United currently accepted for use with the SI in CIPM currently accepts the use of all of States accepts their use with the SI. the United States are given in Table 8. the units given in Table 8 with the SI Nevertheless, use of the corresponding These units, which are subject to future except for the , roentgen, rad, and SI units is encouraged whenever review by the NIST Director on behalf rem. Because of the continued wide use possible, with values given in terms of of the Secretary of Commerce, should be of these units in the United States, the older units in parentheses if defined in relation to the SI in every especially in regulatory documents necessary.

Use of SI Prefixes With Units Outside Rules and Style Conventions name of the unit is derived from the the SI name of a person; and A number of rules and style (b) the preferred symbol for the liter Some SI prefixes are used with some conventions have been adopted in the United States is L. internationally for the use of the SI to of the units given in Tables 6, 7, and 8. 3. When the name of a unit is spelled ensure that scientific and technical For example, prefixes for both positive out, it is always written with a lower- communication is not hindered by and negative powers of ten are used case initial letter unless it begins a ambiguity. The most important of these with the liter, the , the sentence. are as follows: unified atomic mass unit, the bar, and 4. Unit symbols are unaltered in the the barn. Prefixes for positive powers of 1. Unit symbols are printed in roman plural. ten are used with the metric ton, and (upright) type regardless of the type 5. Unit symbols are not followed by prefixes for negative powers of ten are used in the surrounding text. a period unless at the end of a sentence. used with the neper and the bel, 2. Unit symbols are printed in lower- 6. Symbols for units formed from although the bel is most commonly case letters except that: other units by multiplication are used in the form of the : (a) the symbol or the first letter of the indicated by means of a half-high (that 1 dB = 0.1 B. symbol is an upper-case letter when the is, centered) dot or space. 40340 Federal Register / Vol. 63, No. 144 / Tuesday, July 28, 1998 / Notices

Example: N•m or N m juxtaposition of two or more prefix Note: When unit names are spelled out as 7. Symbols for units formed from symbols, are not permitted. This rule is often the case in nontechnical writing, the other units by division are indicated by also applies to compound prefix names. normal rules of English apply. Thus, for example, ‘‘a roll of 35-millimeter film’’ is means of a solidus (oblique stroke,/), a Example: 1 nm (one nanometer) but not: acceptable. horizontal line, or negative exponents. 1 mµm (one millimicrometer) Obsolete Units 11. An SI prefix symbol (and name) − Example: m/s, m , or m⋅ s 1 cannot stand alone, but must always be As stated in the 1990 Federal Register s attached to a unit symbol (or name). notice, metric units, symbols, and terms However, to avoid ambiguity, the Example: 5×106/m3 but not: 5M/m3 that are not in accordance with the solidus must not be repeated on the 12. In the expression for the value of foregoing interpretation are not accepted same line unless parentheses are used. a quantity, the unit symbol is placed for continued use in the United States with the International System of Units. Examples: after the numerical value and a space is m/s2 or m•s¥2 but not: m/s/s left between the numerical value and Accordingly, the following units and m•kg/(s3•A) or m•kg•s¥3•A¥1 but the unit symbol. The only exceptions to terms listed in the table of metric units not: m•kg/s3/A this rule are for the unit symbols for in section 2 of the Act of July 28, 1866 Negative exponents should be used in degree, , and for plane (15 U.S.C. 205) that legalized the metric complicated cases. angle: °, ′, and ′′, respectively (see Table system of weights and measures in the 8. Prefix symbols are printed in roman 6), in which case no space is left United States are not accepted for use in (upright) type regardless of the type between the numerical value and the the United States: used in the surrounding text, and are unit symbol. myriameter attached to unit symbols without a Example: α = 30°22′8′′ stere space between the prefix symbol and millier or tonneau the unit symbol. This last rule also This rule means that: ° quintal applies to prefix names attached to unit (a) The symbol C for the degree names. Celsius is preceded by a space when one myriagram Examples: expresses the values of Celsius kilo (for kilogram). temperatures. 1 mL (one milliliter) Additional Information on the SI 1 pm (one picometer) Example: t = 30.2 °C but not: t = 30.2°C 1 GΩ (one gigaohm) or t = 30.2° C Additional information on the SI may 1 THz (one terahertz) (b) Even when the value of a quantity be found in NIST Special Publication 9. The dgrouping formed by a prefix is used in an adjectival sense, a space (SP) 811, Guide for the Use of the symbol attached to a unit sybmbol is left between the numerical value and International System of Units (SI), by constitutes a new inseparable symbol the unit symbol. (This rule recognizes Barry N. Taylor. This publication is for (forming a multiple or submultiple of that unit symbols are not like ordinary sale by the Superintendent of the unit concerned) which can be raised words or abbreviations but are Documents, but is also available online to a positive or negative and mathematical entities, and that the (as will be this notice) at URL http:// which can be combined with other unit value of a quantity should be expressed physics.nist.gov/cuu. (Although the symbols to form compound unit in a way that is as independent of 1995 edition of SP 811 is the edition symbols. language as possible.) currently available in print and online, Examples: a new edition that fully reflects the Examples: 2.3 cm3 = 2.3 (cm)3 = 2.3 (10¥2 m)3 contents of this notice is under = 2.3×10¥6 m3 a 1 m end gauge but not: a 1-m end preparation and will replace the 1995 1 cm¥1 = 1 (cm)¥1 = 1 (10¥2 m)¥1 gage edition.) 2 ¥1 a 10 kΩ resistance but not: a 10-kΩ = 10 m Although there is no formal comment µ ¥1 µ ¥1 resistance 5000 s = 5000 ( s) period, public comments are welcome ¥6 ¥1 = 5000 (10 s) However, if there is any ambiguity, on a continuing basis. Comments should × 6 ¥1 × 9 ¥1 = 5000 10 s = 5 10 s the words should be rearranged be submitted to Dr. Barry N. Taylor at Prefix names are also inseparable accordingly. For example, the statement the above address. form the unit names to which they are ‘‘the samples were placed in 22 mL Dated: June 19, 1998. attached. Thus, for example, millimeter, vials’’ should be replaced with the micropascal, and meganewton are single statement ‘’the samples were placed in Robert E. Hebner, words. vials of volume 22 mL, ’’ or ‘‘the Acting Deputy Director. 10. Compound prefix symbols, that is, samples were placed in 22 vials of [FR Doc. 98–16965 Filed 7–27–98; 8:45 am] prefix symbols formed by the volume 1 mL,’’ whichever was meant. BILLING CODE 3510±13±M