(See the write-up below this for a current complete list.)

When the metric system was first designed after the French Revolution, the following prefixes were used:

The names from deca to myria are from the Greek names of the numbers, and deci to milli are from the Latin for ten, hundred, and thousand. Alternative symbols for deca have been D and dk, and for myria M was also used — but I don't know how official any of these were. The spelling deka with a K is also used, for distinctness from deci, though the official usage of the BIPM is deca.

The prefixes mega and micro were adopted in 1874; they are from the Greek for big and small respectively. Notice that the origin French system was decimal, in powers of ten. The modern one is not, it is millesimal, in powers of 1000. Now not only are only powers of 1000 given names, but their names are based on this, as will be seen.

Next, in 1960, were the two higher powers giga and tera, from the Greek for giant and monster respectively. At the same time two lower powers were created: nano from the Latin for dwarf, pico from... well my dictionary says pico is Spanish for a small amount, but I'm not convinced that's the whole story.

After that (1964) came femto from femten, Danish for fifteen (as it's 10−15), and atto is from atten eighteen. One suspects there was a Dane on the committee at the time.

There was an asymmetry for many years, which was rectified by the creation in 1975 of peta and exa. These got their names like this. They had run out of great big Greek words, 'big' and 'giant' and 'monster', and they could either turn to classical mythology, or shift to a different language, or what they actually did, reanalyse the names. They decided that tera = 1012 = 10004 looked quite a bit like Greek tetra- = 4. So, as it was now clearly a millesimal system, they arbitrarily deformed penta- = 5 and hexa- = 6 into peta and exa.

Here it stood until 1991. Then they reapplied this principle, but in my opinion, the results were much uglier. They took Latin sept- = 7 and oct- = 8 and deformed them into zepto = 1000−7 and yocto = 1000−8. They then twisted them even more to fit the A-ending pattern of the high powers and created zetta = 10007 and yotta = 10008.

Apart from sheer ugliness, which is subjective, they also used the same letter symbols, lower-case z and y for the small ones and upper-case Z and Y for the large ones — of course in practice no unit could ever take both y and Y in the same context —, and made the psychological mistake (I feel) of using Z as the inner, second-last one, and Y as the last.

I am not aware of any prefixes beyond the current ones ever having been seriously proposed.

Note that symbol for micro is the Greek letter mu, μ. If this symbol is not available in a font it is permissible to use u or mc.

International Electrotechnical Commission (IEC) & SI approved.
International Standard IEC 60027-2

Regular Système International (SI) unit prefixes:

Factor	Prefix 	Symbol  	Factor 	Prefix	 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
Prefixes for binary multiples:
Factor	Name	Symbol	Origin               Derivation
210	kibi	Ki	kilobinary: (210)1   kilo: (103)1
220	mebi	Mi	megabinary: (210)2   mega: (103)2
230	gibi	Gi	gigabinary: (210)3   giga: (103)3
240	tebi	Ti	terabinary: (210)4   tera: (103)4
250	pebi	Pi	petabinary: (210)5   peta: (103)5
260	exbi	Ei	exabinary:  (210)6   exa:  (103)6
Examples and comparisons with SI prefixes:
one kibibit   1 Kibit = 210 bits = 1024 bits
one kilobit   1 kbit  = 103 bits = 1000 bits
one mebibyte  1 MiB   = 220 B    = 1 048 576 B
one megabyte  1 MB    = 106 B    = 1 000 000 B
one gibibyte  1 GiB   = 230 B    = 1 073 741 824 B
one gigabyte  1 GB    = 109 B    = 1 000 000 000 B 

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