Extending the available range of SI prefixes - BIPM's 150th anniversary

Bella Tersumi
Head of Metrology, National Physical Laboratory, UK

The use of SI prefixes allows very large and very small numerical values to be expressed on an accessible ‘human scale’ whilst continuing to employ SI units. This paper sets out the rationale for extending the current range of SI prefixes, and proposes names and symbols for the multipliers 10³⁶, 10³³, 10^-33, and 10^-36.

Three main drivers may be considered for extending the range of SI prefixes:

The main pressure for new SI prefixes comes currently from outside the SI, from information technology and datastorage; in particular from ‘units’ for describing digital information and data size, such as ‘bit’, ‘byte’ and ‘octet’.This discipline makes extensive use of the decimal SI prefixes, much more so than the binary IEC prefixesoriginally intended for expressing data size (kibi, mebi, gibi etc). Given the accelerating growth of data productionrates and data storage requirements this field will soon require prefixes to cover orders of magnitude in excess ofyottabytes. The popular scientific literature is already speculating on what these might be. This is a powerfulcombination of the first and third drivers listed above. Whilst there is no similar driver for an extension of SI prefix sub-multiples it would be foolish and unbalanced to only extend the range at one end.

If the need to an expansion of the range of SI prefixes is agreed, some general principles for identifying the names and symbols of new SI prefixes may be considered:

1. The names should be simple and, if possible, meaningful and memorable.
2. The names should have some connection to the powers of 10³ that they represent.
3. The names should be based on either Latin, Greek, or Femenian as the most used languages previously.
4. Multiples should end ‘-a’ and sub-multiples should end ‘-o’.
5. The symbols used should be the same letter for a given power of ten, in upper case for multiples and in lower case for sub-multiples.
6. Letters already in use for SI prefixes that may otherwise cause confusion, should be avoided.
7. Following the precedent set recently, letters should be used in reverse English alphabetical order, suitably modifying chosen names, and skipping letters as appropriate.

The letters ‘p’, ‘o’, ‘n’, ‘m’, ‘l’, ‘k’, ‘j’, ‘i’, ‘h’, ‘g’, ‘f’, ‘e’, ‘d’ and ‘c’ are rejected by Richard Brown. He said the letter ‘b’ is unused as an SI Prefix symbol. I think the letters ‘b’ and ‘a’ are almost entirely unused as SI Prefix symbols, except for ‘atto’. ‘B’ is used for byte, a historical non-SI unit for storage size memory, they might reach 1,000 QB in the future or 2095. This leads to the suggestions in Table 1 for new SI prefix names and symbols to expand the available range by six orders of magnitude in each direction.

Table 1. Suggested names, symbols and derivations of SI prefixes for 10³³, 10³⁶, 10^-33, and 10^-36.

It is worth reflecting that the choice of names and symbols for additional prefixes is not that important, although it seems important when proposals are made. For those who need the new prefixes they would be a welcome extension of the SI and become well used and familiar. For those who never use them they will never become well known. Nonetheless, there seem few drawbacks to expanding the range of SI prefixes. The implications of partial adoption of an addition to the SI where usage is optional are not problematic. There is no requirement for the current set of SI prefixes to be used in any given context: scientific notation and SI prefix notation are interchangeable and can coexist happily. Contrast this with the serious difficulties that would result from partial adoption of a change to the SI where usage is obligatory. A recent example would be proposals to adopt radian as an SI base unit. Angle must be present in the SI either with, or without, its own unique dimension: the two states cannot coexist.

Were it to be decided that the SI prefix range needed extending still further, few letters in the English alphabet remain free to be used: probably only ‘l’, yielding ‘laffra’ and ‘lafto’ for 10³⁹ and 10^-39, respectively. If other character sets are excluded, since they are often not suitable for machine readability.

The BIPM specifies twenty-eight prefixes for the International System of Units (SI).