An octotrigintillion is equal to \(10^{117}\) in the short scale, or \(10^{228}\) in the long scale by Conway-Wechsler system.[1][2][3][4][5]
In the long scale which is commonly used in France and Germany, \(10^{117}\) is called novemdecilliard.
In Decimal Form[]
Short Scale
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Long Scale
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations[]
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{117}\) | |
| Arrow notation | \(10\uparrow117\) | |
| Steinhaus-Moser Notation | 64[3] | 65[3] |
| Copy notation | 9[117] | 10[59] |
| Taro's multivariable Ackermann function | A(3,385) | A(3,386) |
| Pound-Star Notation | #*(12,12,11,5,2,3,0,3)*8 | #*(13,12,11,5,2,3,0,3)*8 |
| BEAF | {10,117} | |
| Bird's Array Notation | {10,117} | |
| Hyper-E notation | E117 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)[4531] | (0)(0)(0)(0)(0)[4532] |
| Hyperfactorial array notation | 79! | 80! |
| Fast-growing hierarchy | \(f_2(380)\) | \(f_2(381)\) |
| Hardy hierarchy | \(H_{\omega^2}(380)\) | \(H_{\omega^2}(381)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^2+\omega+7}}(10)\) | |
List of prefixed numbers derived from trigintillion[]
| Name | Short scale | Long scale |
|---|---|---|
| untrigintillion | 1096 | 10186 |
| duotrigintillion | 1099 | 10192 |
| trestrigintillion | 10102 | 10198 |
| quattuortrigintillion | 10105 | 10204 |
| quintrigintillion | 10108 | 10210 |
| sestrigintillion | 10111 | 10216 |
| septentrigintillion | 10114 | 10222 |
| octotrigintillion | 10117 | 10228 |
| noventrigintillion | 10120 | 10234 |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Steve Olsen, Big-Ass Numbers
- ↑ The Conway-Wechsler System
- ↑ Extensions to the -illions I: Henkle, Conway, and Rowlett
- ↑ Fish. Conway's zillion numbers, July 25, 2021
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