- Not to be confused with quinquagintillion.
A quinquadragintillion is equal to \(10^{138}\) or \(10^{270}\) in France and Germany by Conway-Wechsler system.[1][2][3][4][5]
In the long scale which is commonly used in France and Germany, \(10^{138}\) is called tresvigintillion.
The lifetime of our universe is about 10 quinquadragintillion years.[6]
Decimal expansion[]
In short scale:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
In long scale:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations[]
For short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{138}\) | |
| Arrow notation | \(10\uparrow138\) | |
| Steinhaus-Moser Notation | 73[3] | 74[3] |
| Copy notation | 9[138] | 1[139] |
| Taro's multivariable Ackermann function | A(3,455) | A(3,456) |
| Pound-Star Notation | #*(3,2,7,11,8,2,9,1)*10 | #*(5,11,7,12,11,1)*16 |
| BEAF | {10,138} | |
| Hyper-E notation | E138 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)[20535] | (0)(0)(0)(0)(0)[20536] |
| Hyperfactorial array notation | 89! | 90! |
| Fast-growing hierarchy | \(f_2(449)\) | \(f_2(450)\) |
| Hardy hierarchy | \(H_{\omega^2}(449)\) | \(H_{\omega^2}(450)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^2+\omega3+8}}(10)\) | |
For long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{270}\) | |
| Arrow notation | \(10\uparrow270\) | |
| Steinhaus-Moser Notation | 128[3] | 129[3] |
| Copy notation | 9[270] | 1[271] |
| Taro's multivariable Ackermann function | A(3,893) | A(3,894) |
| Pound-Star Notation | #*((7101))*10 | #*((7102))*10 |
| BEAF | {10,270} | |
| Hyper-E notation | E270 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)[16548] | (0)(0)(0)(0)(0)(0)[16549] |
| Hyperfactorial array notation | 153! | 154! |
| Fast-growing hierarchy | \(f_2(887)\) | \(f_2(888)\) |
| Hardy hierarchy | \(H_{\omega^2}(887)\) | \(H_{\omega^2}(888)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^22+\omega7}}(10)\) | |
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
- ↑ Steve Olsen, Big-Ass Numbers
- ↑ Extensions to the -illions I: Henkle, Conway, and Rowlett
- ↑ Fish. Conway's zillion numbers, July 25, 2021
- ↑ https://journals.aps.org/prd/pdf/10.1103/PhysRevD.97.056006
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