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SI Brochure: The International System of Units (SI) [8th edition, 2006; updated in 2014]
Stating values of dimensionless quantities, or quantities of dimension one
SI Brochure, Section 5.3.7

    As discussed in Section 2.2.3, the coherent SI unit for dimensionless quantities, also termed quantities of dimension one, is the number one, symbol 1. Values of such quantities are expressed simply as numbers. The unit symbol 1 or unit name "one" are not explicitly shown, nor are special symbols or names given to the unit one, apart from a few exceptions as follows. For the quantity plane angle, the unit one is given the special name radian, symbol rad, and for the quantity solid angle, the unit one is given the special name steradian, symbol sr. For the logarithmic ratio quantities, the special names neper, symbol Np, bel, symbol B, and decibel, symbol dB, are used (see 4.1 and Table 8).

    Because SI prefix symbols can neither be attached to the symbol 1 nor to the name "one", powers of 10 are used to express the values of particularly large or small dimensionless quantities.

    In mathematical expressions, the internationally recognized symbol % (percent) may be used with the SI to represent the number 0.01. Thus, it can be used to express the values of dimensionless quantities. When it is used, a space separates the number and the symbol %. In expressing the values of dimensionless quantities in this way, the symbol % should be used rather than the name "percent".

    In written text, however, the symbol % generally takes the meaning of "parts per hundred".

    Phrases such as "percentage by mass", "percentage by volume", or "percentage by amount of substance" should not be used; the extra information on the quantity should instead be conveyed in the name and symbol for the quantity.

    In expressing the values of dimensionless fractions (e.g. mass fraction, volume fraction, relative uncertainties), the use of a ratio of two units of the same kind is sometimes useful.

    The term "ppm", meaning 10–6 relative value, or 1 in 106, or parts per million, is also used. This is analogous to the meaning of percent as parts per hundred. The terms "parts per billion", and "parts per trillion", and their respective abbreviations "ppb", and "ppt", are also used, but their meanings are language dependent. For this reason the terms ppb and ppt are best avoided. (In English-speaking countries, a billion is now generally taken to be 109 and a trillion to be 1012; however, a billion may still sometimes be interpreted as 1012 and a trillion as 1018. The abbreviation ppt is also sometimes read as parts per thousand, adding further confusion.)

    When any of the terms %, ppm, etc., are used it is important to state the dimensionless quantity whose value is being specified.

    back to Contents

We are pleased to present the updated (2014) 8th edition of the SI Brochure, which defines and presents the Système International d'Unités, the SI (known in English as the International System of Units).

Chapter 1: Introduction

Chapter 2: SI units

Chapter 3: Decimal multiples and submultiples of SI units

  • SI prefixes
  • Factor Name Symbol Factor Name Symbol
    101 deca da 10–1 deci d
    102 hecto h 10–2 centi c
    103 kilo k 10–3 milli m
    106 mega M 10–6 micro µ
    109 giga G 10–9 nano n
    1012 tera T 10–12 pico p
    1015 peta P 10–15 femto f
    1018 exa E 10–18 atto a
    1021 zetta Z 10–21 zepto z
    1024 yotta Y 10–24 yocto y
  • The kilogram

Chapter 4: Units outside the SI

Chapter 5: Writing unit symbols and names, and expressing the values of quantities

General principles for the writing of unit symbols and numbers were first given by the 9th CGPM (1948, Resolution 7). These were subsequently elaborated by ISO, IEC, and other international bodies. As a consequence, there now exists a general consensus on how unit symbols and names, including prefix symbols and names, as well as quantity symbols should be written and used, and how the values of quantities should be expressed. Compliance with these rules and style conventions, the most important of which are presented in this chapter, supports the readability of scientific and technical papers.

Appendix 1: Decisions of the CGPM and the CIPM

This appendix lists those decisions of the CGPM and the CIPM that bear directly upon definitions of the units of the SI, prefixes defined for use as part of the SI, and conventions for the writing of unit symbols and numbers. It is not a complete list of CGPM and CIPM decisions. For a complete list, reference must be made to the BIPM website, successive volumes of the Comptes Rendus des Séances de la Conférence Générale des Poids et Mesures (CR) and Procès-Verbaux des Séances du Comité International des Poids et Mesures (PV) or, for recent decisions, to Metrologia.

Since the SI is not a static convention, but evolves following developments in the science of measurement, some decisions have been abrogated or modified; others have been clarified by additions. In the SI Brochure, a number of notes have been added by the BIPM to make the text more understandable; they do not form part of the original text.

In the printed brochure, the decisions of the CGPM and CIPM are listed in strict chronological order in order to preserve the continuity with which they were taken. However in order to make it easy to locate decisions related to particular topics a table of contents is also provided, ordered by subject:

Appendix 2: Practical realization of the definitions of some important units

Appendix 3: Units for photochemical and photobiological quantities

Optical radiation is able to cause chemical changes in certain living or non-living materials: this property is called actinism, and radiation capable of causing such changes is referred to as actinic radiation. Actinic radiation has the fundamental characteristic that, at the molecular level, one photon interacts with one molecule to alter or break the molecule into new molecular species. It is therefore possible to define specific photochemical or photobiological quantities in terms of the result of optical radiation on the associated chemical or biological receptors.

In the field of metrology, the only photobiological quantity which has been formally defined for measurement in the SI is for the interaction of light with the human eye in vision. An SI base unit, the candela, has been defined for this important photobiological quantity. Several other photometric quantities with units derived from the candela have also been defined (such as the lumen and the lux, see Table 3 in Chapter 2).