-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,..., 10^2ⁿ, and so on. Today the corresponding Chinese characters are used for 10⁴, 10⁸, 10¹², 10¹⁶, and so on.

Details and examples

In Knuth's -yllion proposal:

1 to 999 still have their usual names.
1000 to 9999 are divided before the 2nd-last digit and named "foo hundred bar."
10⁴ to 10⁸ − 1 are divided before the 4th-last digit and named "foo myriad bar". Knuth also introduces at this level a grouping symbol for the numeral. So 382,1902 is "three hundred eighty-two myriad nineteen hundred two."
10⁸ to 10¹⁶ − 1 are divided before the 8th-last digit and named "foo myllion bar", and a semicolon separates the digits. So 1,0002;0003,0004 is "one myriad two myllion, three myriad four."
10¹⁶ to 10³² − 1 are divided before the 16th-last digit and named "foo byllion bar", and a colon separates the digits. So 12:0003,0004;0506,7089 is "twelve byllion, three myriad four myllion, five hundred six myriad seventy hundred eighty-nine."
etc.

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 Ancient Greek numeral system, and also the Chinese "short scale", "myriad scale", and "mid scale". Today these Chinese 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.

Value	Name	Notation	Standard English name	Ancient Greek	Chinese	Pīnyīn	Jyutping	Pe̍h-ōe-jī
10⁰	One	1	One	εἷς	一	yī	jat¹	it/chit
10¹	Ten	10	Ten	δέκα	十	shí	sap⁶	si̍p/cha̍p
10²	One hundred	100	One hundred	ἑκατόν	百	bǎi	baak³	pah
10³	Ten hundred	1000	One thousand	χίλιοι	千	qiān	cin¹	chhian
10⁴	One myriad	1,0000	Ten thousand	μύριοι	萬, 万	wàn	maan⁶	bān
10⁵	Ten myriad	10,0000	One hundred thousand	δεκάκις μύριοι	十萬, 十万	shíwàn	sap⁶ maan⁶	si̍p/cha̍p bān
10⁶	One hundred myriad	100,0000	One million	ἑκατοντάκις μύριοι	百萬, 百万	bǎiwàn	baak³ maan⁶	pah bān
10⁷	Ten hundred myriad	1000,0000	Ten million	χιλιάκις μύριοι	千萬, 千万	qiānwàn	cin¹ maan⁶	chhian bān
10⁸	One myllion	1;0000,0000	One hundred million	μυριάκις μύριοι	億, 亿	yì	jik¹	ek
10⁹	Ten myllion	10;0000,0000	One billion	δεκάκις μυριάκις μύριοι	十億, 十亿	shíyì	sap⁶ jik¹	si̍p/cha̍p ek
10¹⁰	One hundred myllion	100;0000,0000	Ten billion	ἑκατοντάκις μυριάκις μύριοι	百億, 百亿	bǎiyì	baak³ jik¹	pah ek
10¹¹	Ten hundred myllion	1000;0000,0000	One hundred billion	χῑλῐάκῐς μυριάκις μύριοι	千億, 千亿	qiānyì	cin¹ jik¹	chhian ek
10¹²	One myriad myllion	1,0000;0000,0000	One trillion	μυριάκις μυριάκις μύριοι	萬億, 万亿	wànyì	maan⁶ jik¹	bān ek
10¹³	Ten myriad myllion	10,0000;0000,0000	Ten trillion	δεκάκις μυριάκις μυριάκις μύριοι	十萬億, 十万亿	shíwànyì	sap⁶ maan⁶ jik¹	si̍p/cha̍p bān ek
10¹⁴	One hundred myriad myllion	100,0000;0000,0000	One hundred trillion	ἑκατοντάκις μυριάκις μυριάκις μύριοι	百萬億, 百万亿	bǎiwànyì	baak³ maan⁶ jik¹	pah bān ek
10¹⁵	Ten hundred myriad myllion	1000,0000;0000,0000	One quadrillion	χιλιάκις μυριάκις μυριάκις μύριοι	千萬億, 千万亿	qiānwànyì	cin¹ maan⁶ jik¹	chhian bān ek
10¹⁶	One byllion	1:0000,0000;0000,0000	Ten quadrillion	μυριάκις μυριάκις μυριάκις μύριοι	兆	zhào	siu⁶	tiāu
10²⁴	One myllion byllion	1;0000,0000:0000,0000;0000,0000	One septillion	μυριάκις μυριάκις μυριάκις μυριάκις μυριάκις μύριοι	億兆, 亿兆	yìzhào	jik¹ siu⁶	ek tiāu
10³²	One tryllion	1'0000,0000;0000,0000:0000,0000;0000,0000	One hundred nonillion	μυριάκις μυριάκις μυριάκις μυριάκις μυριάκις μυριάκις μυριάκις μύριοι	京	jīng	ging¹	kiaⁿ
10⁶⁴	One quadryllion		Ten vigintillion		垓	gāi	goi¹	kai
10¹²⁸	One quintyllion		One hundred unquadragintillion		秭	zǐ	zi²	chi
10²⁵⁶	One sextyllion		Ten quattuoroctogintillion		穰	ráng	joeng⁴	liōng
10⁵¹²	One septyllion		One hundred novensexagintacentillion		溝, 沟	gōu	kau¹	kau
10¹⁰²⁴	One octyllion		Ten quadragintatrecentillion		澗, 涧	jiàn	gaan³	kán
10²⁰⁴⁸	One nonyllion		One hundred unoctogintasescentillion		正	zhēng	zing³	chiàⁿ
10⁴⁰⁹⁶	One decyllion		Ten milliquattuorsexagintatrecentillion		載, 载	zài	zoi³	chài

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.

Negative powers

To refer to small quantities with this system, the suffix -th is used.
For instance, is a myriadth.
is a ''vigintyllionth.''