- Not to be confused with duocentillion.
Ducentillion or dihectillion[1] is equal to 10603 in short scale and 101,200 in long scale.[2] The name is equal with Conway-Wechsler System,[3] but it seems to be developed independently.
Landon Curt Noll coined the name duocentillion for this number (not to be confused with Bowers' duocentillion, which equals 10309).[4][5]
Aarex Tiaokhiao gave the name bicemillion, referring to the value of this number.[6]
BlankEntity calls this number Ceedol.[7]
It is 604 digits long in short scale, or 1,201 digits long in long scale.
Written out in decimal form ducentillion (in the short scale) is:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
In long scale:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations
For short scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{603}\) | |
| Arrow notation | \(10\uparrow603\) | |
| Steinhaus-Moser Notation | 251[3] | 252[3] |
| Copy notation | 9[603] | 10[302] |
| Chained arrow notation | \(10\rightarrow603\) | |
| H* function | H(200) | |
| Taro's multivariable Ackermann function | A(3,2000) | A(3,2001) |
| Pound-Star Notation | #*((147))*15 | #*((148))*15 |
| BEAF & Bird's array notation | {10,603} | |
| Hyper-E notation | E603 | |
| Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)[51396] | (0)(0)(0)(0)(0)(0)(0)[51397] |
| Hyperfactorial array notation | 295! | 296! |
| Fast-growing hierarchy | \(f_2(1992)\) | \(f_2(1993)\) |
| Hardy hierarchy | \(H_{\omega^2}(1992)\) | \(H_{\omega^2}(1993)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^26+3}}(10)\) | |
For long scale:
| Notation | Lower bound | Upper bound |
|---|---|---|
| Scientific notation | \(1\times10^{1200}\) | |
| Arrow notation | \(10\uparrow1200\) | |
| Steinhaus-Moser Notation | 451[3] | 452[3] |
| Copy notation | 9[1200] | 1[1201] |
| Taro's multivariable Ackermann function | A(3,3983) | A(3,3984) |
| Pound-Star Notation | #*((1182))*20 | #*((1183))*20 |
| BEAF | {10,1200} | |
| Hyper-E notation | E1200 | |
| Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
| Hyperfactorial array notation | 524! | 525! |
| Fast-growing hierarchy | \(f_2(3974)\) | \(f_2(3975)\) |
| Hardy hierarchy | \(H_{\omega^2}(3974)\) | \(H_{\omega^2}(3975)\) |
| Slow-growing hierarchy | \(g_{\omega^{\omega^3+\omega^22}}(10)\) | |
Sources
- ↑ https://sites.google.com/site/aarexnumbers/home/ch2/at1i
- ↑ Illion Numbers
- ↑ [1]
- ↑ English names of the first 10000 powers of 10 - American System without dashes
- ↑ English names of the first 10000 powers of 10 - European System without dashes
- ↑ Aarex Tiaokhiao's illion numbers[dead link]
- ↑ BlankEntity's Googology Site
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
