Systematic Numeric Nomenclature: Dozenal (SNN_z) (also known as Systematic Dozenal Nomenclature (SDN)) provides a set of dozenal power prefixes (usable with any metrology) that are analogous to the decimal metric scaling prefixes of the International System of Units (SI). However, SNN_z does not require an international committee to generate higher and higher order prefixes. Instead, it derives its prefixes systematically from a set of twelve familiar Greek and Latin numeric roots, each directly expressing the exponent in a power of twelve. These roots are identical to those used by the International Union of Pure and Applied Chemistry (IUPAC) to construct Systematic Element Names, extended to support dozenal base with the addition of two roots, dec and lev, to represent ten and eleven as single dozenal digits (ᘔ and Ɛ). IUPAC chose its roots carefully so that they all begin with unique letters, making them amenable to single-character abbreviations. The dozenal additions maintain this uniqueness.

Multiplier and Power Prefixes

SNN_z provides not only power prefixes, but also accommodates multiplier prefixes, which are existing combination forms of the numeric roots, keeping intact their common meanings as simple multipliers. To avoid clashing with these forms, the power prefixes are derived by appending distinct syllables onto the roots: -qua· (abbreviated with an upwards arrow ↑) for positive powers, and -cia· (abbreviated with an downwards arrow ↓) for negative powers. These endings are entirely novel, and will not be confused with any pre-existing usage of these numeric roots. Further, the contrast between the hard q versus the soft c, plus the rounded u versus the fronted i, ensures that positive and negative powers will not be confused with each other.

The following table lists the roots, the existing multiplier prefixes, and the corresponding power prefixes:

One consequence of this scheme is that the first negative power prefix, uncia·, is identical to the ancient Latin word uncia, which had the exact same meaning.

Multidigit Prefixes

When a multiplier contains multiple digits, or when the exponent of a power contains multiple digits, SNN_z expresses these by concatenating digit roots. This relies on exactly the same place-value arithmetic principle that Hindu-Arabic numerals employ. The final digit is then terminated as either a multiplier or power form; this determines the form for the whole string. So for example, the following table shows the multiplier and power prefixes corresponding to the next three values beyond eleven:

Because the power prefixes are distinct from the multiplier forms, both can be freely combined without ambiguity, to create an analog of scientific notation. So for instance:

• bihexpenta· (bhp•) represents 265_z
• bihexa·pentqua· (bh•p↑) represents 26×10⁵_z
• bina·hexpentqua· (b•hp↑) represents 2×10⁶⁵_z
• bihexpentqua· (bhp↑) represents 10²⁶⁵_z

Fractional Mantissas

To completely represent scientific notation, we need one additional lexical element, to represent a fraction point. SNN_z uses the syllable .dot. for this purpose (abbreviated with the usual period). Hence:

• bihexa·pentqua· (bh•p↑), representing 26×10⁵_z, can also be expressed as:
• bi.dot.hexa·hexqua· (b.h•h↑), representing 2.6×10⁶_z. 

A multiplier digit is only required to the right of dot. If there is no digit to the left, it is assumed to be nil (0). So for example:

• dot.hexa· (.h•) represents 0.6_z, i.e., a half.

Reciprocals

SNN_z also provides a set of reciprocal prefixes, representing the reciprocals of multiplier prefixes. These make use of the marking suffix -infra· (abbreviated with a backslash \ ), which derives directly from the Latin word infra, which means "below" or "under". The sense is that the preceding digits are being placed in the denominator of a rational number, under the horizontal line. For example:

• one fifth can be expressed as pentinfra· (p\)
• one seventh can be expressed as septinfra· (s\)
• and so forth.

These can be freely combined with the ordinary multiplier prefixes to express any rational number. Thus, 5/7 (or 5•7\) could be expressed as penta·septinfra· (p•s\). Interestingly, these reciprocal prefixes act as distinct multiplicative factors, so there is no order dependency like there would be with an actual division operator. Hence 5/7 could be expressed equivalently as septinfra·penta· (s\p•). This will not be confused with 7/5, because that would be expressed as septa·pentinfra· (s•p\), or pentinfra·septa· (p\s•).

The syllable per- can be combined with powers of dozen to provide dozenal analogs of decimal percent (%) and permille (‰). Dozenalists have often expressed these as "pergross" and "per great-gross". However, in SNN_z, these can be pronounced perbiqua· and pertriqua·. To some extent these are redundant with bicia· and tricia·, but it is often helpful to think of a fraction as a number of parts from a group. So for example, a ratio of 1/3 could be expressed as 40%_z ("four dozen perbiqua·") or even 400‰_z ("four gross pertriqua·"). This could be extended to any power of dozen, so for instance analogs for "parts per million", "parts per billion", "parts per trillion", etc., could be expressed as perhexqua·, perennqua·, perunnilqua·, etc. 

The Middle Dot

Note that each SNN_z prefix expresses some factor which the following unit is multiplied by. This is true not only of the multiplier prefixes, but also of the reciprocal and power prefixes. When such prefixes are concatenated, the effect is to take the product of the factors they represent. Accordingly, this wiki uses the convention of terminating each SNN_z prefix with a middle dot (·) character (Unicode U+00B7_x). This resembles the dot operator ( ⋅ ) character (Unicode U+22C5_x), which conveys the notion of multiplication; however, some fonts render the latter with extra whitespace around the dot, which is desirable in mathematical expressions, but not in word forms.

Abbreviations

See child page Abbreviations for Systematic Numeric Prefixes for an explanation of the suggested abbreviations for the prefixes.

Pronunciations

See child page Pronunciation of Systematic Numeric Prefixes for suggested pronunciations for the prefixes.