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

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:

[email protected]

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 T0 = 273.15 K, the ice point. This

temperature difference is called Celsius temperature, symbol t, and is

defined by the quantity equation t = T-T0. 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 t and the thermodynamic temperature

difference T between the melting point of gallium and the

triple point of water may be written as t = 29.7546 deg.C =

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: Nm 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/s2 or ms-2 but not: m/s/s

mkg/(s3A) or

mkgs-3A-1 but not:

mkg/s3/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 (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 cm3 = 2.3 (cm)3 = 2.3 (10-2

m)3 = 2.3 x 10-6 m3

1 cm-1 = 1 (cm)-1 = 1 (10-2

m)-1 = 102 m-1

5000 s-1 = 5000 (s)-1 = 5000

(10-6 s)-1 = 5000 x 106 s-1

= 5 x 109 s-1

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 mm (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 106/m3 but not: 5M/m3

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: = 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 resistance but not: a 10-k 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]

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