Ducentillion

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Not to be confused with duocentillion.

A ducentillion is equal to \(10^{603}\) in the short scale and \(10^{1200}\) in the long scale by the Conway and Guy's naming system^[1]^[2]^[3]^[4]^[5] or by Jonathan Bowers system^[6] as it is the 200th -illion number.

In the long scale, \(10^{603}\) is called centilliard.

Landon Curt Noll coined the name duocentillion for this number (not to be confused with Conway and Bowers' duocentillion, which equals 10³⁰⁹ in the short scale).^[7]^[8]

Aarex Tiaokhiao gave the name bicemillion^[9] or dihectillion,^[10] referring to the value of this number.

BlankEntity calls this number Ceedol.^[11]

Decimal expansion[]

Written out in decimal form ducentillion (in the short scale) is:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

In long scale:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Approximations[]

For the short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{603}\) (exact)
Arrow notation	\(10\uparrow 603\) (exact)
Steinhaus-Moser Notation	251[3]	252[3]
Chained arrow notation	\(10\rightarrow 603\) (exact)
Taro's multivariable Ackermann function	A(3,2000)	A(3,2001)
BEAF & Bird's array notation	{10,603} (exact)
Hyper-E notation	E603 (exact)
s(n) map	\(s(1)^3(\lambda x.x+1)(7)\)	\(s(1)^3(\lambda x.x+1)(8)\)
m(n) map	m(1)(251)	m(1)(252)
Bashicu matrix system	(0)(0)(0)(0)(0)(0)(0)(0)(0)[15]	(0)(0)(0)(0)(0)(0)(0)(0)(0)[16]
Copy notation	9[603]	10[302]
H* function	H(200)
Pound-Star Notation	#((147))15	#((148))15
Hyperfactorial array notation	295!	296!
Fast-growing hierarchy	\(f_2(1992)\)	\(f_2(1993)\)
Hardy hierarchy	\(H_{\omega^2}(1992)\)	\(H_{\omega^2}(1993)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^2 6+3}}(10)\) (exact)

For the long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{1200}\) (exact)
Arrow notation	\(10\uparrow 1200\) (exact)
Steinhaus-Moser Notation	451[3]	452[3]
Chained arrow notation	\(10\rightarrow 1200\) (exact)
Taro's multivariable Ackermann function	A(3,3983)	A(3,3984)
BEAF & Bird's array notation	{10,1200} (exact)
Hyper-E notation	E1200 (exact)
s(n) map	\(s(1)^3(\lambda x.x+1)(8)\)	\(s(1)^3(\lambda x.x+1)(9)\)
m(n) map	m(1)(451)	m(1)(452)
Bashicu matrix system	(0)(1)[3]	(0)(1)[4]
Copy notation	9[1200]	1[1201]
Pound-Star Notation	#((1182))20	#((1183))20
Hyperfactorial array notation	524!	525!
Fast-growing hierarchy	\(f_2(3974)\)	\(f_2(3975)\)
Hardy hierarchy	\(H_{\omega^2}(3974)\)	\(H_{\omega^2}(3975)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^3+\omega^2 2}}(10)\) (exact)

Sources[]

↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-18.
↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-18.
↑ Fish. Conway's zillion numbers. Retrieved 2023-02-18.
↑ Fish. Conway's illion converter - 10^603. Retrieved 2023-02-18.
↑ Illion Numbers
↑ English names of the first 10000 powers of 10 - American System without dashes
↑ English names of the first 10000 powers of 10 - European System without dashes
↑ Aarex Tiaokhiao's illion numbers^{[dead link]}
↑ https://sites.google.com/site/aarexnumbers/home/ch2/at1i^{[dead link]}
↑ BlankEntity's Googology Site

See also[]

Standard -illion numbers 10³ⁿ⁺³ (10⁶ⁿ)

Main article: -illion

1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non
10–19: decillion · undec · duodec · tredec · quattuordec · quindec · sexdec · septendec · octodec · novemdec
20–29: vigintillion · unvigint · duovigint · tresvigint · quattuorvigint · quinvigint · sesvigint · septemvigint · octovigint · novemvigint
30–39: trigintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
40–49: quadragintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
50–59: quinquagintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
60–69: sexagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
70–79: septuagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
80–89: octogintillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
90–99: nonagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
100–900: centillion · ducent · trecent · quadringent · quingent · sescent · septingent · octingent · nongent
1,000–10³⁰: millillion · dumill · dumillinonagintanongent · trimill · trimilliduotrigintatrecent · trimillisexoctogintaoctingent · quadrimill · quadrimilliquattuordecicent · quinmill · sexmill · septimill · octimill · nonimill · myr · decimilliquinsexagintasescent · dumyr · unquadragintamilliunquinquagintacent · centimill · micr · nan · pic · femt · att · zept · yoct · ront · quect

Standard -ducentillion numbers 10⁶⁰³ (10¹²⁰⁰)

Main article: -illion

[1] Conway and Guy. (1995) "The book of Numbers" Copernicus

[2] Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-18.

[3] Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-18.

[fish-4] Fish. Conway's zillion numbers. Retrieved 2023-02-18.

[5] Fish. Conway's illion converter - 10^603. Retrieved 2023-02-18.

[6] Illion Numbers

[7] English names of the first 10000 powers of 10 - American System without dashes

[8] English names of the first 10000 powers of 10 - European System without dashes

[9] Aarex Tiaokhiao's illion numbers^{[dead link]}

[10] ttps://sites.google.com/site/aarexnumbers/home/ch2/at1i^{[dead link]}

[11] BlankEntity's Googology Site

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