An octogintillion is equal to 10243 in short scale, or 10480 in the long scale by Conway and Guy's naming system[1][2][3][4] or Jonathan Bowers system.[5] This number has 244 digits.
In the long scale which is commonly used in France and Germany, 10243 is called quadragintilliard.
Contents
Approximations
For short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{243}\) | |
| Arrow notation | \(10\uparrow243\) | |
| Steinhaus-Moser Notation | 117[3] | 118[3] |
| Copy notation | 9[243] | 10[122] |
| Taro's multivariable Ackermann function | A(3,804) | A(3,805) |
| Pound-Star Notation | #*((269))*10 | #*((270))*10 |
| BEAF | {10,243} | |
| Hyper-E notation | E243 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)[6264] | (0)(0)(0)(0)(0)(0)[6265] |
| Hyperfactorial array notation | 140! | 141! |
| Fast-growing hierarchy | \(f_2(797)\) | \(f_2(798)\) |
| Hardy hierarchy | \(H_{\omega^2}(797)\) | \(H_{\omega^2}(798)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^22+\omega4+3}}(10)\) | |
For long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{480}\) | |
| Arrow notation | \(10\uparrow480\) | |
| Steinhaus-Moser Notation | 207[3] | 208[3] |
| Copy notation | 9[480] | 1[481] |
| Taro's multivariable Ackermann function | A(3,1591) | A(3,1592) |
| Pound-Star Notation | #*((7))*14 | #*((8))*14 |
| BEAF | {10,480} | |
| Hyper-E notation | E480 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)[5623] | (0)(0)(0)(0)(0)(0)(0)[5624] |
| Hyperfactorial array notation | 244! | 245! |
| Fast-growing hierarchy | \(f_2(1583)\) | \(f_2(1584)\) |
| Hardy hierarchy | \(H_{\omega^2}(1583)\) | \(H_{\omega^2}(1584)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^24+\omega8}}(10)\) | |
List of prefixed numbers derived from octogintillion
| Name | Short scale | Long scale |
|---|---|---|
| unoctogintillion | 10246 | 10486 |
| duooctogintillion | 10249 | 10492 |
| treoctogintillion | 10252 | 10498 |
| quattuoroctogintillion | 10255 | 10504 |
| quinoctogintillion | 10258 | 10510 |
| sexoctogintillion | 10261 | 10516 |
| septenoctogintillion | 10264 | 10522 |
| octooctogintillion | 10267 | 10528 |
| novemoctogintillion | 10270 | 10534 |
Sources
- ↑ Big-Ass Numbers
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ The Conway-Wechsler System
- ↑ Conway's zillion numbers. Retrieved 2021-08-01.
- ↑ Bowers, Jonathan. Illion Numbers. Retrieved 2021-08-01.
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 · trevigint · quattuorvigint · quinvigint · sexvigint · septenvigint · octovigint · novemvigint
30–39: trigintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
40–49: quadragintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
50–59: quinquagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
60–69: sexagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
70–79: septuagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
80–89: octogintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
90–99: nonagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
100–900: centillion · unviginticent · unsexagintacent · ducent · trecent · duotrigintatrecent · quadringent · quingent · sescent · septuagintisescent · 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
