A nongentillion is equal to \(10^{2703}\) in the short scale and \(10^{5400}\) in the long scale by the Conway and Guy's naming system[1][2][3][4][5] and Jonathan Bower's system[6] as it is the 900th -illion number.
In the long scale, \(10^{2703}\) is called quinquagintaquadringentilliard.[7]
Decimal expansion[]
Written out in decimal form nongentillion (in the short scale) is:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
In long scale:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations[]
For the short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{2703}\) (exact) | |
| Arrow notation | \(10\uparrow 2703\) (exact) | |
| Steinhaus-Moser Notation | 913[3] | 914[3] |
| Chained arrow notation | \(10\rightarrow 2703\) (exact) | |
| Taro's multivariable Ackermann function | A(3,8976) | A(3,8977) |
| BEAF & Bird's array notation | {10,2703} (exact) | |
| Hyper-E notation | E2703 (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)(913) | m(1)(914) |
| Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
| Copy notation | 9[2703] | 10[1352] |
| Pound-Star Notation | #*((101))*29 | #*((102))*29 |
| Hyperfactorial array notation | 1044! | 1045! |
| Fast-growing hierarchy | \(f_2(8966)\) | \(f_2(8967)\) |
| Hardy hierarchy | \(H_{\omega^2}(8966)\) | \(H_{\omega^2}(8967)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^3 2+\omega^2 7+3}}(10)\) (exact) | |
For the long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{5400}\) (exact) | |
| Arrow notation | \(10\uparrow 5400\) (exact) | |
| Steinhaus-Moser Notation | 1674[3] | 1675[3] |
| Chained arrow notation | \(10\rightarrow 5400\) (exact) | |
| Taro's multivariable Ackermann function | A(3,17935) | A(3,17936) |
| BEAF & Bird's array notation | {10,5400} (exact) | |
| Hyper-E notation | E5400 (exact) | |
| s(n) map | \(s(1)^3(\lambda x.x+1)(10)\) | \(s(1)^3(\lambda x.x+1)(11)\) |
| m(n) map | m(1)(1674) | m(1)(1675) |
| Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
| Copy notation | 9[5400] | 1[5401] |
| Pound-Star Notation | #*((3445))*39 | #*((3446))*39 |
| Hyperfactorial array notation | 1898! | 1899! |
| Fast-growing hierarchy | \(f_2(17924)\) | \(f_2(17925)\) |
| Hardy hierarchy | \(H_{\omega^2}(17924)\) | \(H_{\omega^2}(17925)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^3 5+\omega^2 4}}(10)\) (exact) | |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-10-04.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-10-04.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-10-04.
- ↑ Fish. Conway's illion converter - 10^2703. Retrieved 2023-10-04.
- ↑ Illion Numbers by Jonathan Bowers
- ↑ Fish. Conway's illion converter - 10^2703 (long scale). Retrieved 2023-10-04.
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
1,000–1030: 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
Main article: -illion
900–909: nongentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)910–919: decinongentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
920–929: vigintinongentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
930–939: trigintanongentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
940–949: quadragintanongentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
950–959: quinquagintanongentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
960–969: sexagintanongentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
970–979: septuagintanongentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
980–989: octogintanongentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
990–999: nonagintanongentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)