[Federal Register Volume 63, Number 144 (Tuesday, July 28, 1998)]
[Notices]
[Pages 40334-40340]
From the Federal Register Online via the Government Publishing Office [www.gpo.gov]
[FR Doc No: 98-16965]



[[Page 40333]]

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Part II





Department of Commerce





_______________________________________________________________________



National Institute of Standards and Technology



_______________________________________________________________________



Metric System of Measurement: Interpretation of the International 
System of Units for the United States; Notice

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

[[Page 40334]]



DEPARTMENT OF COMMERCE

National Institute of Standards and Technology
[Docket No. 980430113-8113-01]


Metric System of Measurement: Interpretation of the International 
System of Units for the United States

AGENCY: National Institute of Standards and Technology, Commerce.

ACTION: Notice.

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SUMMARY: This notice restates the interpretation of the International 
System of Units (SI) for the United States by the Department of 
Commerce. This interpretation was last published by the Department of 
Commerce in the Federal Register on December 20, 1990 (55 FR 52242-
52245). Since the publication of that notice, the international bodies 
that are responsible for the SI have made some changes to it. It has 
therefore become necessary to set forth a new interpretation of the SI 
for the United States that reflects these changes.

FOR FURTHER INFORMATION CONTACT: For information regarding the 
International System of Units, contact Dr. Barry N. Taylor, Building 
225, Room B161, National Institute of Standards and Technology, 
Gaithersburg, MD 20899-0001, telephone number (301) 975-4220. For 
information regarding the Federal Government's efforts to coordinate 
the transition of the United States to the International System of 
Units, contact Mr. James B. McCracken, Metric Program, Building 820, 
Room 306, National Institute of Standards and Technology, Gaithersburg, 
MD 20899-0001, telephone number (301) 975-3690, email: 
<a href="/cdn-cgi/l/email-protection#94f9f1e0e6fdf7cbcbe4e6f3d4fafde7e0baf3fbe2"><span class="__cf_email__" data-cfemail="97faf2e3e5fef4c8c8e7e5f0d7f9fee4e3b9f0f8e1">[email protected]</span></a>

SUPPLEMENTARY INFORMATION: Section 5164 of Public Law 100-418, the 
Omnibus Trade and Competitiveness Act of 1988, amended Public Law 94-
168, the Metric Conversion Act of 1975. In particular, section 3 of the 
Metric Conversion Act (codified as amended 15 U.S.C. 205b) reads as 
follows:
    ``Sec. 3. It is therefore the declared policy of the United 
States--
    ``(1) to designate the metric system of measurement as the 
preferred system of weights and measures for United States trade and 
commerce;
    ``(2) to require that each Federal agency, by a date certain and to 
the extent economically feasible by the end of the fiscal year 1992, 
use the metric system of measurement in its procurements, grants, and 
other business related activities, except to the extent that such use 
is impractical or is likely to cause significant inefficiencies or loss 
of markets to United States firms, such as when foreign competitors are 
producing competing products in non-metric units;
    ``(3) to seek out ways to increase understanding of the metric 
system of measurement through educational information and guidance and 
in Government publications; and
    ``(4) to permit the continued use of traditional systems of weights 
and measures in nonbusiness activities.''
    In the Metric Conversion Act of 1975, the ``metric system of 
measurement'' is defined as the International System of Units as 
established in 1960 by the General Conference of Weights and Measures 
(abbreviated CGPM after the French Conference General des Poids et 
Mesures) and interpreted or modified for the United States by the 
Secretary of Commerce (15 U.S.C. 205c). The Secretary has delegated 
this authority to the Director of the National Institute of Standards 
and Technology. In implementation of this authority, tables and 
associated text were published in the Federal Register of December 20, 
1990 (55 FR 52242-52245), setting forth the interpretation for the 
United States of the International System of Units (abbreviated SI in 
all languages after the French Systeme International d'Unites).
    The CGPM is an intergovernmental organization established by the 
Meter Convention (Convention du Metre), which was signed by the United 
States and 16 other countries in Paris in 1875 (nearly 50 countries are 
now members of the Convention). One of the responsibilities of the CGPM 
is to ensure that the SI reflects the latest advances in science and 
technology. Since the publication of the 1990 Federal Register notice, 
the CGPM has made two significant changes to the SI. These are (1) the 
addition of four new SI prefixes to form decimal multiples and 
submultiples of SI units; and (2) the elimination of the class of 
supplementary units (the radian and the steradian) as a separate class 
in the SI. Further, the International Committee for Weights and 
Measures (abbreviated CIPM after the French Comite International des 
Poids et Mesures), which comes under the authority of the CGPM, has 
made some new recommendations regarding units not part of the SI that 
may be used with the SI. It is therefore necessary to issue new tables 
and associated text that reflect these changes and which set forth a 
new interpretation of the SI for the United States. Thus this Federal 
Register notice supersedes the previous interpretation published in the 
Federal Register on December 20, 1990 (55 FR 52242-52245).

Classes of SI Units

    There are now only two classes of units in the International System 
of Units: base units and derived units. The units of these two classes 
form a coherent set of units and are designated by the name ``SI 
units.'' Here, the term coherent is used to mean a unit system where 
all derived units are obtained from the base units by the rules of 
multiplication and division with no numerical factor other than the 
number 1 ever occurring in the expressions for the derived units in 
terms of the base units. The SI also includes prefixes to form decimal 
multiples and submultiples of SI units. Because units formed with SI 
prefixes are not coherent with SI units, the units so formed are 
designated by their complete name ``decimal multiples and submultiples 
of SI units'' in order to make a distinction between them and the 
coherent set of SI units proper. The SI units and their decimal 
multiples and submultiples together are often called ``units of the 
SI.''

SI Base Units

    The SI is founded on seven SI base units for seven base quantities 
assumed to be mutually independent. These units and quantities are 
given in Table 1.


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SI Derived Units

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

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Quantities of Dimension 1

    The last entry of Table 2, mass fraction, is an example of certain 
derived quantities that are defined as the ratio of two mutually 
comparable quantities, that is, two quantities of the same kind. Since 
the coherent SI derived unit of such a derived quantity is the ratio of 
two identical SI units, that unit may also be expressed by the number 
one, symbol 1. Such quantities are called quantities of dimension 1, or 
dimensionless quantities, and the SI unit of all such quantities is the 
number 1. Examples of other derived quantities of dimension 1, and thus 
with a coherent SI derived unit that may be expressed by the number 1, 
are relative permeability, dynamic friction factor, refractive index, 
characteristic numbers such as the Mach number, and numbers that 
represent a count, such as a number of molecules. However, the number 1 
is generally not explicitly shown in the expression for the value of a 
quantity of dimension 1. For example, the value of the refractive index 
of a given medium is expressed as n = 1.51 rather than as n = 1.51  x  
1. In a few cases a special name and symbol are given to the number 1 
to aid understanding. The radian, unit symbol rad, and steradian, unit 
symbol sr, which are given in Table 3 and are discussed in connection 
with Table 4, are two such examples.

SI Derived Units With Special Names and Symbols

    For ease of understanding and convenience, 21 SI derived units have 
been given special names and symbols. These are listed in Table 3, 
where it should be noted that the last three units of Table 3, the 
becquerel, unit symbol Bq, the gray, unit symbol Gy, and the sievert, 
unit symbol Sv, were specifically introduced by the CGPM with a view to 
safeguarding human health.


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Degree Celsius

    The derived unit in Table 3 with special name degree Celsius and 
special symbol  deg.C deserves comment. Because of the way temperature 
scales used to be defined, it remains common practice to express a 
thermodynamic temperature, symbol T, in terms of its difference from 
the reference temperature T<INF>0</INF> = 273.15 K, the ice point. This 
temperature difference is called Celsius temperature, symbol t, and is 
defined by the quantity equation t = T-T<INF>0</INF>. The unit of 
Celsius temperature is the degree Celsius, symbol  deg.C. The numerical 
value of a Celsius temperature t expressed in degrees Celsius is given 
by

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It follows from the definition of t that the degree Celsius is equal in 
magnitude to the kelvin, which in turn implies that the numerical value 
of a given temperature difference or temperature interval whose value 
is expressed in the unit degree Celsius ( deg.C) is equal to the 
numerical value of the same difference or interval when its value is 
expressed in the unit kelvin (K). Thus temperature differences or 
temperature intervals may be expressed in either the degree Celsius or 
the kelvin using the same numerical value. For example, the Celsius 
temperature difference <greek-D>t and the thermodynamic temperature 
difference <greek-D>T between the melting point of gallium and the 
triple point of water may be written as <greek-D>t = 29.7546  deg.C = 
<greek-D>T = 29.7546 K. (Note that the centigrade temperature scale is 
obsolete; the unit name degree centigrade should no longer be used.)

Use of SI Derived Units With Special Names and Symbols

    The special names and symbols of the 21 SI derived units with 
special names and symbols given in Table 3 may themselves be included 
in the names and symbols of other SI derived units. This use is shown 
in Table 4. All of the SI derived units in Table 4, like those in Table 
3, have been obtained from the SI base units in the same coherent 
manner discussed above.


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Radian and Steradian

    As indicated in Table 3, the radian, unit symbol rad, and 
steradian, unit symbol sr, are the special names and symbols for the 
derived units of plane angle and solid angle, respectively. These units 
may be used or not in expressions for derived units as is convenient in 
order to distinguish between derived quantities that are not of the 
same kind but are of the same dimension (that is, derived quantities 
whose units when expressed in SI base units are the same). Table 4 
includes some examples of derived units that use the radian and 
steradian.

SI Prefixes

    Table 5 gives the 20 SI prefixes used to form decimal multiples and 
submultiples of SI units. It is important to note that the kilogram is 
the only SI unit with a prefix as part of its name and symbol. Because 
multiple prefixes may not be used, in the case of the kilogram the 
prefix names of Table 5 are used with the unit name ``gram'' and the 
prefix symbols are used with the unit symbol ``g.'' With this 
exception, any SI prefix may be used with any SI unit, including the 
degree Celsius and its symbol  deg.C.


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    Because the SI prefixes strictly represent powers of 10, it is 
inappropriate to use them to represent powers of 2. Thus 1 kbit = 10\3\ 
bit = 1000 bit and not 2\10\ = 1024 bit, where 1 kbit is one kilobit.

Units Outside the SI

    Certain units are not part of the International System of Units, 
that is, they are outside the SI, but are important and widely used. 
Consistent with the recommendations of the CIPM, the units in this 
category that are accepted for use in the United States with the SI are 
given in Tables 6 and 7.

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Liter and Metric Ton

    The units liter and metric ton in Table 6 deserve comment. The 
liter and its symbol l were adopted by the CIPM in 1879. The 
alternative symbol for the liter, L, was adopted by the CGPM in 1979 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 preferred symbol for use 
in the United States is L. Neither a lowercase script letter l nor an 
uppercase script letter l are approved symbols for the liter. With 
regard to the metric ton, this is the name to be used in the United 
States for the unit with symbol t and defined according to 1 t = 10\3\ 
kg. (The name ``metric ton'' is also used in some other English 
speaking countries, but the name ``tonne'' is used in many countries.)


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Other Units Outside the SI

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

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Use of SI Prefixes With Units Outside the SI

    Some SI prefixes are used with some of the units given in Tables 6, 
7, and 8. For example, prefixes for both positive and negative powers 
of ten are used with the liter, the electronvolt, the unified atomic 
mass unit, the bar, and the barn. Prefixes for positive powers of ten 
are used with the metric ton, and prefixes for negative powers of ten 
are used with the neper and the bel, although the bel is most commonly 
used in the form of the decibel: 1 dB = 0.1 B.

Rules and Style Conventions

    A number of rules and style conventions have been adopted 
internationally for the use of the SI to ensure that scientific and 
technical communication is not hindered by ambiguity. The most 
important of these are as follows:
    1. Unit symbols are printed in roman (upright) type regardless of 
the type used in the surrounding text.
    2. Unit symbols are printed in lower-case letters except that:
    (a) the symbol or the first letter of the symbol is an upper-case 
letter when the name of the unit is derived from the name of a person; 
and
    (b) the preferred symbol for the liter in the United States is L.
    3. When the name of a unit is spelled out, it is always written 
with a lower-case initial letter unless it begins a sentence.
    4. Unit symbols are unaltered in the plural.
    5. Unit symbols are not followed by a period unless at the end of a 
sentence.
    6. Symbols for units formed from other units by multiplication are 
indicated by means of a half-high (that is, centered) dot or space.


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Example: N<bullet>m or N m

    7. Symbols for units formed from other units by division are 
indicated by means of a solidus (oblique stroke,/), a horizontal line, 
or negative exponents.

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    However, to avoid ambiguity, the solidus must not be repeated on 
the same line unless parentheses are used.

Examples:
    m/s<SUP>2</SUP> or m<bullet>s<SUP>-2</SUP> but not: m/s/s
    m<bullet>kg/(s<SUP>3</SUP><bullet>A) or 
m<bullet>kg<bullet>s<SUP>-3</SUP><bullet>A<SUP>-1</SUP> but not: 
m<bullet>kg/s<SUP>3</SUP>/A

    Negative exponents should be used in complicated cases.
    8. Prefix 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 prefix names attached to unit names.

Examples:
    1 mL (one milliliter)
    1 pm (one picometer)
    1 G<greek-OH> (one gigaohm)
    1 THz (one terahertz)

    9. The dgrouping formed by a prefix symbol attached to a unit 
sybmbol constitutes a new inseparable symbol (forming a multiple or 
submultiple of the unit concerned) which can be raised to a positive or 
negative power and which can be combined with other unit symbols to 
form compound unit symbols.

Examples:
    2.3 cm<SUP>3</SUP> = 2.3 (cm)<SUP>3</SUP> = 2.3 (10<SUP>-2</SUP> 
m)<SUP>3</SUP> = 2.3 x 10<SUP>-6</SUP> m<SUP>3</SUP>
    1 cm<SUP>-1</SUP> = 1 (cm)<SUP>-1</SUP> = 1 (10<SUP>-2</SUP> 
m)<SUP>-1</SUP> = 10<SUP>2</SUP> m<SUP>-1</SUP>
5000 <greek-m>s<SUP>-1</SUP> = 5000 (<greek-m>s)<SUP>-1</SUP> = 5000 
(10<SUP>-6</SUP> s)<SUP>-1</SUP> = 5000 x 10<SUP>6</SUP> s<SUP>-1</SUP> 
= 5 x 10<SUP>9</SUP> s<SUP>-1</SUP>

    Prefix names are also inseparable form the unit names to which they 
are attached. Thus, for example, millimeter, micropascal, and 
meganewton are single words.
    10. 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 prefix names.

Example:  1 nm (one nanometer) but not: 1 m<greek-m>m (one 
millimicrometer)

    11. An SI prefix symbol (and name) cannot stand alone, but must 
always be attached to a unit symbol (or name).

Example:  5 x 10<SUP>6</SUP>/m<SUP>3</SUP> but not: 5M/m<SUP>3</SUP>

    12. 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:  deg., ', and '', respectively (see Table 6), in which case no 
space is left between the numerical value and the unit symbol.

Example: <greek-a> = 30 deg.22'8''

    This rule means that:
    (a) The symbol  deg.C for the degree Celsius is preceded by a space 
when one expresses the values of Celsius temperatures.

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

    (b) 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 1 m end gauge but not: a 1-m end gage
    a 10 k<greek-OH> resistance but not: a 10-k<greek-OH> resistance

    However, if there is any ambiguity, the words should be rearranged 
accordingly. For example, the statement ``the samples were placed in 22 
mL vials'' should be replaced with the statement `'the samples were 
placed in vials of volume 22 mL, '' or ``the samples were placed in 22 
vials of volume 1 mL,'' whichever was meant.

    Note: When unit names are spelled out as is often the case in 
nontechnical writing, the normal rules of English apply. Thus, for 
example, ``a roll of 35-millimeter film'' is acceptable.

Obsolete Units

    As stated in the 1990 Federal Register notice, metric units, 
symbols, and terms that are not in accordance with the foregoing 
interpretation are not accepted for continued use in the United States 
with the International System of Units. Accordingly, the following 
units and terms listed in the table of metric units in section 2 of the 
Act of July 28, 1866 (15 U.S.C. 205) that legalized the metric system 
of weights and measures in the United States are not accepted for use 
in the United States:

myriameter
stere
millier or tonneau
quintal
myriagram
kilo (for kilogram).

Additional Information on the SI

    Additional information on the SI may be found in NIST Special 
Publication (SP) 811, Guide for the Use of the International System of 
Units (SI), by Barry N. Taylor. This publication is for sale by the 
Superintendent of Documents, but is also available online (as will be 
this notice) at URL http://physics.nist.gov/cuu. (Although the 1995 
edition of SP 811 is the edition currently available in print and 
online, a new edition that fully reflects the contents of this notice 
is under preparation and will replace the 1995 edition.)
    Although there is no formal comment period, public comments are 
welcome on a continuing basis. Comments should be submitted to Dr. 
Barry N. Taylor at the above address.

    Dated: June 19, 1998.
Robert E. Hebner,
Acting Deputy Director.
[FR Doc. 98-16965 Filed 7-27-98; 8:45 am]
BILLING CODE 3510-13-M


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