Quadringentillion

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A quadringentillion is equal to \(10^{1203}\) in the short scale and \(10^{2400}\) in the long scale by the Conway and Guy's naming system^[1]^[2]^[3]^[4]^[5] and Jonathan Bowers naming system^[6] as it is the 400th -illion number.

In the long scale, \(10^{1203}\) is called ducentilliard.^[7]

Decimal expansion[]

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

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

In the long scale:

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Approximations[]

For the short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{1203}\) (exact)
Arrow notation	\(10\uparrow 1203\) (exact)
Steinhaus-Moser Notation	452[3]	453[3]
Chained arrow notation	\(10\rightarrow 1203\) (exact)
Taro's multivariable Ackermann function	A(3,3993)	A(3,3994)
BEAF & Bird's array notation	{10,1203} (exact)
Hyper-E notation	E1203 (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)(452)	m(1)(453)
Copy notation	9[1203]	10[602]
Pound-Star Notation	#((1411))20	#((1412))20
Hyperfactorial array notation	525!	526!
Bashicu matrix system	(0)(1)[3]	(0)(1)[4]
Fast-growing hierarchy	\(f_2(3984)\)	\(f_2(3985)\)
Hardy hierarchy	\(H_{\omega^2}(3984)\)	\(H_{\omega^2}(3985)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^3+\omega^2 2+3}}(10)\) (exact)

For the long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{2400}\) (exact)
Arrow notation	\(10\uparrow 2400\) (exact)
Steinhaus-Moser Notation	823[3]	824[3]
Chained arrow notation	\(10\rightarrow 2400\) (exact)
Taro's multivariable Ackermann function	A(3,7969)	A(3,7970)
BEAF & Bird's array notation	{10,2400} (exact)
Hyper-E notation	E2400 (exact)
s(n) map	\(s(1)^3(\lambda x.x+1)(9)\)	\(s(1)^3(\lambda x.x+1)(10)\)
m(n) map	m(1)(823)	m(1)(824)
Bashicu matrix system	(0)(1)[3]	(0)(1)[4]
Copy notation	9[2400]	1[2401]
Pound-Star Notation	#((8572))27	#((8573))27
Hyperfactorial array notation	943!	944!
Fast-growing hierarchy	\(f_2(7959)\)	\(f_2(7960)\)
Hardy hierarchy	\(H_{\omega^2}(7959)\)	\(H_{\omega^2}(7960)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^3 2+\omega^2 4}}(10)\) (exact)

Sources[]

↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-03-10.
↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-03-10.
↑ Fish. Conway's zillion numbers. Retrieved 2023-03-10.
↑ Fish. Conway's illion converter - 10^1203. Retrieved 2023-03-10.
↑ Illion Numbers by Jonathan Bowers
↑ Fish. Conway's illion converter - 10^1203 (long scale). Retrieved 2023-03-10.

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 -quadringentillion numbers 10¹²⁰³ (10²⁴⁰⁰)

Main article: -illion

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

[2] Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-03-10.

[3] Olsen, Steve. Big-Ass Numbers. Retrieved 2023-03-10.

[fish-4] Fish. Conway's zillion numbers. Retrieved 2023-03-10.

[5] Fish. Conway's illion converter - 10^1203. Retrieved 2023-03-10.

[6] Illion Numbers by Jonathan Bowers

[7] Fish. Conway's illion converter - 10^1203 (long scale). Retrieved 2023-03-10.

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