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Writing unit symbols and names, and expressing the values of quantities
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Unit symbols
Unit names
Rules and style conventions for expressing values of quantities

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Section 5.3.1
Sections 5.3.2--5.3.6
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SI brochure, Section 5.3 cont.

5.3.7 Stating values of dimensionless quantities, or quantities of dimension one

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.

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Related articles

Section 5.3.1
Sections 5.3.2--5.3.6

Note: For the official text, please refer to the PDF files available at:
  • (in English) and
  • (in French).