A duotrigintatrecentillion is equal to \(10^{999}\) in the short scale and \(10^{1992}\) in the long scale by the Conway and Guy's naming system[1][2][3][4][5] as it is the 332nd -illion number.
In the long scale, \(10^{999}\) is called sesexagintacentilliard.
Sbiis Saibian named \(10^{999}\) as trecenti-triginti-deutillion in the short scale and centi-sexaginti-sextilliard in the long scale.[6]
Duotrigintatrecentillion is also known as trecenduotrigintillion according to Landon Curt Noll's naming system.[7]
Decimal expansion[]
Written out in decimal form duotrigintatrecentillion (in the short scale) is:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
In the long scale:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations[]
For the short scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{999}\) (exact) | |
Arrow notation | \(10\uparrow 999\) (exact) | |
Steinhaus-Moser Notation | 386[3] | 387[3] |
Chained arrow notation | \(10\rightarrow 999\) (exact) | |
Taro's multivariable Ackermann function | A(3,3315) | A(3,3316) |
BEAF & Bird's array notation | {10,999} (exact) | |
Hyper-E notation | E999 (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)(386) | m(1)(387) |
Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
Copy notation | 9[999] | 10[500] |
Pound-Star Notation | #*((14))*19 | #*((15))*19 |
H* function | H(332) | |
Hyperfactorial array notation | 449! | 450! |
Fast-growing hierarchy | \(f_2(3306)\) | \(f_2(3307)\) |
Hardy hierarchy | \(H_{\omega^2}(3306)\) | \(H_{\omega^2}(3307)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^2 9+\omega 9+9}}(10)\) (exact) |
For the long scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{1992}\) (exact) | |
Arrow notation | \(10\uparrow 1992\) (exact) | |
Steinhaus-Moser Notation | 700[3] | 701[3] |
Chained arrow notation | \(10\rightarrow 1992\) (exact) | |
Taro's multivariable Ackermann function | A(3,6614) | A(3,6615) |
BEAF & Bird's array notation | {10,1992} (exact) | |
Hyper-E notation | E1992 (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)(700) | m(1)(701) |
Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
Copy notation | 9[1992] | 1[1993] |
Pound-Star Notation | #*((1993))*25 | #*((1994))*25 |
Hyperfactorial array notation | 805! | 806! |
Fast-growing hierarchy | \(f_2(6604)\) | \(f_2(6605)\) |
Hardy hierarchy | \(H_{\omega^2}(6604)\) | \(H_{\omega^2}(6605)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^3+\omega^2 9+\omega 9+2}}(10)\) (exact) |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-28.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-28.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-02-28.
- ↑ Fish. Conway's illion converter - 10^999. Retrieved 2023-02-28.
- ↑ Sbiis Saibian. Ultimate Large Number List Retrieved 2023-02-28.
- ↑ Landon Curt Noll. The English name of a number Retrieved 2023-02-28.
See also[]
Main article: -illion
1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non10–19: 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
300–309: trecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)310–319: decitrecentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
320–329: vigintitrecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
330–339: trigintatrecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
340–349: quadragintatrecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
350–359: quinquagintatrecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
360–369: sexagintatrecentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
370–379: septuagintatrecentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
380–389: octogintatrecentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
390–399: nonagintatrecentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)