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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[]

  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.
  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.

See also[]

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
1,000–1024: 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
Main article: -illion
400–409: quadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
410–419: deciquadringentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
420–429: vigintiquadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
430–439: trigintaquadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
440–449: quadragintaquadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
450–459: quinquagintaquadringentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
460–469: sexagintaquadringentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
470–479: septuagintaquadringentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
480–489: octogintaquadringentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
490–499: nonagintaquadringentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
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