"Large" Numbers: My Own System

An experienced googologist knows that there are many systems for naming -illions. I am going to add my own to the list, for no real reason.

Small -illions are the same as they are in the canonical system. They will be listed here, for completeness.

1000x+1	Name
0	Thousand
1	Million
2	Billion
3	Trillion
4	Quadrillion
5	Pentillion
6	Sextillion
7	Septillion
8	Octillion
9	Nonillion
10	Decillion
11	Undecillion
12	Duodecillion
13	Tredecillion
14	Quattuordecillion
15	Quindecillion
16	Sexdecillion
17	Septendecillion
18	Octodecillion
19	Novemdecillion
20	Vigintillion

Does this go up to a usefully high amount? Of course not! A vigintillion, wrote out in decimal form, is a mere 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 (10⁶³, E63, or <10,63> depending on which notation you prefer). It doesn't even approach the number of m³ in a Mpc³, let alone larger numbers.

Following the trend set by "decillion", it is trivial to extend the numbers up to 10⁹⁰.

1000x+1	Name
21	Unvigintillion
22	Duovigintillion
23	Trevigintillion
24	Quattuorvigintillion
25	Quinvigintillion
26	Sexvigintillion
27	Septenvigintillion
28	Octoviginitillion
29	Novemvigintillion

Are these so high they are useless? Not at all! Looking at Wikipedia's page on orders of magnitude, it looks like we still need to beat decimal32 floating point numbers (the canonical prefixes beat 32-bit binary numbers, with a mere three hundred and fourty undecillion, two hundred and eighty two decillion and three hundred and fourty nonillion the highest number expressible). Anyway, we seem to have reached a roadblock, given that there is no word for 1000³¹ in the canonical prefixes. However, this is easily fixed, by looking at etymology.

The word "vigintillion" is formed from the Latin word "vīgintī", meaning twenty. To find the next "-illion", we simply find the Latin word for 30, which happens to be "trīgintā". Application is simple:

1000x+1	Name
30	Trigintillion

With -illions number 31 through 39 being constructed in the same way as 21 through 29 and 11 through 19. But why stop at 30? The romans had numbers up to 1,000 (M), and these can easily be used as prefixes for numbers up to 1000¹⁰⁰¹. Given that many people can't count in Latin, I'll include the names of the -illions from 40 to 100 here. Intermediates can be generated as normal.

1000x+1	Name
40	Quadragintillion
50	Quinquagintillion
60	Sexagintillion
70	Septuagintillion
80	Octogintillion
90	Nonagintillion
100	Centillion
101	Uncentillion
111	Undecentillion (Un-dec-centillion)
200	Duocentillion
300	Trecentillion
400	Quadringentillion
500	Quingentillion
600	Sescentillion
700	Septingentillion
800	Octigentillion
900	Nongentillion
999	Novemonaginongentillion (Novem-nonagint-nongentillion)
1000	Millillion

Now, we reach a second roadblock. The Romans had no reason to use numbers over 1000 (pfft, ameutures) and hence haven't named them with single words(they still have notation for it though, which increases at a rate of 1000^x, and they can also express larger numbers by saying them directly, like "eight thousand"). In my next post, I will describe how roman numbers can be extended to stretch beyond 1000 (mīlle), and up to the low -illions.

One last thought for this post:

1000x+1	-illion Name	1/x	SI Prefix
10	decillion	10	deci-
100	centillion	100	centi-
1000	millillion	1000	milli-
106	???	106	micro-

--Thomas