A quattuorquadragintillion is equal to 10135 in the short scale, or \(10^{264}\) in the long scaleby Conway-Wechsler system[1][2][3][4] or Jonathan Bowers system.[5]
In the long scale which is commonly used in France and Germany, \(10^{135}\) is called duovigintilliard.
Decimal expansion[]
In short scale:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
In long scale:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations[]
For short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{135}\) | |
| Arrow notation | \(10\uparrow135\) | |
| Steinhaus-Moser Notation | 72[3] | 73[3] |
| Copy notation | 9[135] | 10[68] |
| Taro's multivariable Ackermann function | A(3,445) | A(3,446) |
| Pound-Star Notation | #*(1,14,10,5,0,9,2,1)*10 | #*(9,5,13,6,3,0,3)*12 |
| BEAF | {10,135} | |
| Hyper-E notation | E135 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)[16548] | (0)(0)(0)(0)(0)[16549] |
| Hyperfactorial array notation | 88! | 89! |
| Fast-growing hierarchy | \(f_2(439)\) | \(f_2(440)\) |
| Hardy hierarchy | \(H_{\omega^2}(439)\) | \(H_{\omega^2}(440)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^2+\omega3+5}}(10)\) | |
For long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{264}\) | |
| Arrow notation | \(10\uparrow264\) | |
| Steinhaus-Moser Notation | 125[3] | 126[3] |
| Copy notation | 9[264] | 1[265] |
| Taro's multivariable Ackermann function | A(3,873) | A(3,874) |
| Pound-Star Notation | #*((3432))*10 | #*((3433))*10 |
| BEAF | {10,264} | |
| Hyper-E notation | E264 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)[13335] | (0)(0)(0)(0)(0)(0)[13336] |
| Hyperfactorial array notation | 150! | 151! |
| Fast-growing hierarchy | \(f_2(867)\) | \(f_2(868)\) |
| Hardy hierarchy | \(H_{\omega^2}(867)\) | \(H_{\omega^2}(868)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^22+\omega6+4}}(10)\) | |
List of prefixed numbers derived from quadragintillion[]
| Name | Short scale | Long scale |
|---|---|---|
| unquadragintillion | 10126 | 10246 |
| duoquadragintillion | 10129 | 10252 |
| tresquadragintillion | 10132 | 10258 |
| quattuorquadragintillion | 10135 | 10264 |
| quinquadragintillion | 10138 | 10270 |
| sesquadragintillion | 10141 | 10276 |
| septenquadragintillion | 10144 | 10282 |
| octoquadragintillion | 10147 | 10288 |
| novenquadragintillion | 10150 | 10294 |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ The Conway-Wechsler System
- ↑ Extensions to the -illions I: Henkle, Conway, and Rowlett
- ↑ Fish. Conway's zillion numbers, July 25, 2021
- ↑ Saibian, Sbiis. 2.4.8 Bowers' -illions - Large 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 · 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