I almost gave this an (even) clickbait-ier title, like SI prefixes are weirder than you think or The story of SI prefixes just gets sadder and sadder. I resisted, but really, you can't make this stuff up.
Thanks to Moore's law (the usual shorthand for a number of factors), compugeeks now find themselves using words like exabyte from time to time. What's an exabyte? It's either 1018 bytes, that is 1,000,000,000,000,000,000 bytes, or 260 bytes, that is 1,152,921,504,606,846,976, though technically that's an exbibyte. In any case, it's a lot, more or less a million terabyte disks.
How did we get to the point of using words like exagram or exbibyte, and where is this all headed? Let's have a look at the full list of SI prefixes. The "short scale" in the third column is the system that says billion rather than thousand million, commonly used in the US and I'm not sure where else.
| Prefix | Size | Short scale | Adoption |
|---|---|---|---|
| quecto- (q) | 10-30 | nonillionth | 2022 |
| ronto- (r) | 10-27 | octillionth | 2022 |
| yocto- (y) | 10-24 | septillionth | 1991 |
| zepto- (z) | 10-21 | sextillionth | 1991 |
| atto- (a) | 10-18 | quintillionth | 1964 |
| femto- (f) | 10-15 | quadrillionth | 1964 |
| pico- (p) | 10-12 | trillionth | 1960 |
| nano- (n) | 10-12 | billionth | 1960 |
| micro- (µ) | 10-12 | millionth | 1960 |
| myria- (ma or my) | 10-4 | ten-thousandth | 1795 dropped in 1960 |
| milli- (m) | 10-3 | thousandth | 1795 |
| centi- (c) | 10-2 | hundredth | 1795 |
| deci- (d) | 10-1 | tenth | 1795 |
| deca- (da) | 101 | ten | 1795 |
| hecto- (H) | 102 | hundred | 1795 |
| kilo- (K) | 103 | thousand | 1795 |
| myrio- (mo) | 104 | ten-thousand | 1795 dropped in 1960 |
| mega- (M) | 106 | million | 1960 |
| giga- (G) | 109 | billion | 1960 |
| tera- (T) | 1012 | trillion | 1960 |
| peta- (P) | 1015 | quadrillion | 1975 |
| exa- (E) | 1018 | quintillion | 1975 |
| zetta- (Z) | 1021 | sextillion | 1991 |
| yotta- (Y) | 1024 | septillion | 1991 |
| ronna- (R) | 1027 | octillion | 2022 |
| quetta- (Q) | 1030 | nonillion | 2022 |
The main milestones that led to this list were
- The original definitions of myria-,milli-,centi-,deci-,deca-,hecto-,kilo- and myrio- in 1795, ratified in 1889 by the General Conference on Weights and Measures (CGPM), which has been the governing body since then.
- The 1960 changes, which dropped myria- and myrio- and added mega-, giga-, tera-, micro-, nano- and pico-.
- The addition of femto- and atto- in 1964
- The addition of peta- and exa- in 1975
- The addition of zetta-, yotta-, zepto- and yocto- in 1991
- The addition of ronna-, quetta, ronto- and quecto- in 2022
The original definitions simply codified the usage of the time. The metric system was a European development intended, like many European developments of the time, to be the standard worldwide. European scientific terms were generally drawn from Greek and Latin roots, not always in any particular order, giving us terms like insectology (insect from Latin, logos from Greek) or capillary (Latin capillus for hair + Greek -ary, belonging to).
In other words, most if not all of the original prefixes would have been easily understandable by a typical European natural philosopher of the time, who would have had at least a basic knowledge of Classical Latin and Greek. Several are still in use in other contexts, in words like decade, century, cent and mile. While myriad is not a common word, it's still used here and there to mean "a whole lot", if not precisely 10,000, and then there are more specialized words like decagon or millipede.
This worked fine for quite a while. The first major change came in 1960. Besides the new words, there was a change in approach. Rather than trying to have a name for every power of ten, the system would have a name for every third power of ten, that is to say every power of a thousand, corresponding to the use of commas (or other delimiters) in writing numbers. The prefixes for ten/tenth and hundred/hundredth were kept since they were in wide use (except perhaps hecto-), but myrio-/myria- were dropped in favor of mega-/micro for million/millionth. Along with these came giga-/nano- for billion/billionth and tera-/pico- for trillion/trillionth.
Since Classical number systems didn't have well-established ways of going beyond tens of thousands, the committee picked various words for big and small:
- mega- comes from the Greek for big, and micro- for small. These were widely in use in other scientific or medical terms like megalomania and microscope
- giga- comes from the Greek for giant, as in gigantic
- nano- comes from the Greek for dwarf
- tera- comes from the Greek for monster, so "monstrously large"
- pico- comes from the Spanish for a tiny bit, also cognate with beak
Though all of these are still in use, this approach of using different words for big and small has its drawbacks. How do you know that pico- is smaller than nano- or that tera- is bigger than giga-?
There's also the matter of all those ms: We already have milli- starting with m. Using mega- isn't a problem, since multiples get capital letters while submultiples get lowercase, but how do you abbreviate micro-? The committee chose the greek letter mu (µ), which was no problem to write by hand but a bit inconvenient on a modern keyboard, to the point that people often cheat and use u. This wouldn't be the last headache around abbreviation, or even the first, considering that deca- is officially abbreviated da and not D.
The next round of changes, in 1964, abandoned the idea of finding more and more ways to say "big" and "small". Instead, prefixes would indicate the power of ten. A quadrillionth is 10-15 , so the prefix for it is based on the number fifteen, in particular, the Danish (also Swedish and Norwegian) femten, for fifteen. Similarly, atto- for 10-18, is from Danish atten, meaning eighteen. Why Danish? There looks to be an interesting story behind that, but I'm not going to take time to run that down at the moment.
This approach of indicating the power of ten in Danish didn't last long. The next additions, peta- and exa- in 1975, reverted to Greek and, instead of counting powers of ten, counted powers of a thousand or, equivalently, counted the commas in the full number. A quadrillion is 1015, that is, 10005, and peta- is penta- without the n. Likewise, a quintillion is 1018, that is, 10006, and exa- is hexa- without the h. Actually using penta- and hexa- would have been confusing, but using something close to them has (perhaps) some mnemonic value. In the case of exa- leaving off the h also avoids a collision with hecto-.
It's a useful coincidence, but just a coincidence, that tera- is tetra- (four) without the second t. On the other hand, it's potentially confusing that the short scale terms for the sizes are off by one compared to the prefixes. That is, peta- stands for quadrillion and not quintillion, because the short scale billion really ought to be trillion, and so on.
So far, we have prefixes for everything up to 1015 in either direction, and an approach that could naturally extend farther, which is exactly what happened in 1991. The new prefixes are zetta-, close to sept for seven, yotta, close(-ish) to oct for eight, paired with zepto- and yocto- for the submultiples. The first letters z and y reflect a new approach to avoiding collisions with other prefixes or common abbreviations: Go backward through the alphabet, skipping anything that's already in use. The committee decided that z and y weren't too likely to cause confusion.
This was a somewhat arbitrary choice. In reality, all the letters of the Latin and Greek alphabets are used for something. For example, x, y and z typically denote the dimensions of a three-dimensional space. Nonetheless, the 1991 additions make a fair bit of sense: The multiple and submultiple have the same root and the same letter abbreviation, capital for the multiple and lowercase for the submultiple. The names even mean something, once you know the key. Given all the constraints, this is a pretty good result.
At this point, the letters in use were
- H,K,M,G,T,P,E,Z and Y for multiples (plus D if you use that instead of da for deca-)
- d,c,m,µ,n,p,f,a,z and y for submultiples
If you require the letters for multiple and submultiple to match, you need to avoid
- a,c,d,e,f,g,h,k,m,n,p,t,y,z
That leaves
- b,i,j,l,o,q,r,s,u,v,w,x
You probably want to rule out i,l and o since they look like 1 or 0. The 2022 committee also ruled out x, since it's very often used as a variable. It also ruled out v, w and s since they're used for Volt, Watt and second (though mm for millimeter doesn't seem to confuse anyone). They ruled out u because it often denotes potential energy and/or because of the common use of u as a cheat for µ. The next two letters in reverse alphabetical order are r and q.
The committee came up with ronna- and ronto- for 1027, which are kind of close to "r combined with ennea (Greek for nine) and maybe to nona- as in nonagon". But 1030 was trickier. The root would mean ten, which was already used for ... ten. Combining with an initial q resulted in a multiple that sounds bad in Portuguese, so the multiple ended up quetta- and the submultiple quecto-. If you know what to look for, quecto- suggests "deca with a q", but quetta is more than a bit of a stretch. It's also spelled the same as a prominent city in Pakistan (this might or might not be coincidence), but it's meant to be pronounced with a hard k sound, as though it were spelled in Spanish, so KEHT-ah and KEHK-toh.
What comes next? After q, assuming we don't want o because of confusion with zero, l because of confusion with one (lowercase) and liter (uppercase), j because of confusion with Joule (uppercase), i because of confusion with one (capital) or the imaginary unit (lowercase), you're left with b, which you would then combine with a root meaning eleven, but both Greek and Latin use "one-ten" for eleven, so ... maybe benno- and becto-? And then what?
But it turns out that the main driver for this is in quantifying data storage. The "global datasphere", meaning the total of all data stored worldwide, is currently running into the zetta- range, and the unit of data storage is the byte, denoted by b. If we can't use b, we're out of letters anyway. That hasn't stopped some compugeeks from suggesting bronto- (as well as hella-), but as far as the standards committee is concerned, quetta-/quecto- is probably as far as we go.
And besides, a 64-bit address space ought to be enough for anyone ... oh, wait ...
As a practical matter, people tend to rescale once the numbers get too mind-numbingly big. For example, astronomers use earth mass (about 6 ronnagrams, but more likely 6 zettatonnes), solar mass (about 2 ronnatonnes), parsec (about 31 petameters) and so on. These in turn can grow prefixes -- megaparsecs (Mpc) and gigaparsecs (Gpc) are both in common use. For comparison, the observable universe is about 14Gpc across and the Saggitarius A* black hole at the center of the Milky Way is about 4.3 million solar masses (not referred to as mega- anything). As convenient as a powers-of-ten scale is, people still tend to use units that make sense to them.
