-yllion


-yllion is a proposal from Donald Knuth for the terminology and symbols of an alternate decimal superbase system. In it, he adapts the familiar English terms for large numbers to provide a systematic set of names for much larger numbers. In addition to providing an extended range, -yllion also dodges the long and short scale ambiguity of -illion.
Knuth's digit grouping is exponential instead of linear; each division doubles the number of digits handled, whereas the familiar system only adds three or six more. His system is basically the same as one of the ancient and now-unused Chinese numeral systems, in which units stand for 104, 108, 1016, 1032,..., 102n, and so on. Today the corresponding characters are used for 104, 108, 1012, 1016, and so on.

Details and examples

In Knuth's -yllion proposal:
Each new number name is the square of the previous one — therefore, each new name covers twice as many digits. Knuth continues borrowing the traditional names changing "illion" to "yllion" on each one.
Abstractly, then, "one n-yllion" is. "One trigintyllion" would have 232+1, or 42;9496,7297, or nearly forty-three myllion digits. Better yet, "one centyllion" would have 2102+1, or 507,0602;4009,1291:7605,9868;1282,1505, or about 1/20 of a tryllion digits, whereas a conventional "centillion" has only 304 digits.
The corresponding Chinese "long scale" numerals are given, with the traditional form listed before the simplified form. Same numerals are used in the Chinese "short scale", "myriad scale", and "mid scale". Today these numerals are still in use, but are used in their "myriad scale" values, which is also used in Japanese and in Korean. For a more extensive table, see Myriad system.
ValueNameNotationStandard English name Chinese Pīnyīn Jyutping Pe̍h-ōe-jī
100One1One一yījat1it/chit
101Ten10Ten十shísap6si̍p/cha̍p
102One hundred100One hundred百bǎibaak3pah
103Ten hundred1000One thousand千qiāncin1chhian
104One myriad1,0000Ten thousand萬, 万wànmaan6bān
105Ten myriad10,0000One hundred thousand十萬, 十万shíwànsap6 maan6si̍p/cha̍p bān
106One hundred myriad100,0000One million百萬, 百万bǎiwànbaak3 maan6pah bān
107Ten hundred myriad1000,0000Ten million千萬, 千万qiānwàncin1 maan6chhian bān
108One myllion1;0000,0000One hundred million億, 亿yìjik1ek
109Ten myllion10;0000,0000One billion十億, 十亿shíyìsap6 jik1si̍p/cha̍p ek
1012One myriad myllion1,0000;0000,0000One trillion萬億, 万亿wànyìmaan6 jik1bān ek
1016One byllion1:0000,0000;0000,0000Ten quadrillion兆zhàosiu6tiāu
1024One myllion byllion1;0000,0000:0000,0000;0000,0000One septillion億兆, 亿兆yìzhàojik1 siu6ek tiāu
1032One tryllion1'0000,0000;0000,0000:0000,0000;0000,0000One hundred nonillion京jīngging1kiaⁿ
1064One quadryllionTen vigintillion垓gāigoi1kai
10128One quintyllionOne hundred unquadragintillion秭zǐzi2chi
10256One sextyllionTen quattuoroctogintillion穰rángjoeng4liōng
10512One septyllionOne hundred novensexagintacentillion溝, 沟gōukau1kau
101024One octyllionTen quadragintatrecentillion澗, 涧jiàngaan3kán
102048One nonyllionOne hundred unoctogintasescentillion正zhēngzing3chiàⁿ
104096One decyllionTen milliquattuorsexagintatrecentillion載, 载zàizoi3chài

Latin- prefix

In order to construct names of the form n-yllion for large values of n, Knuth appends the prefix "latin-" to the name of n without spaces and uses that as the prefix for n. For example, the number "latintwohundredyllion" corresponds to n = 200, and hence to the number.