- Not to be confused with trescentillion.
A trecentillion is equal to \(10^{903}\) in the short scale and \(10^{1800}\) in the long scale by the Conway and Guy's naming system[1][2][3][4][5] as it is the 300th -illion number.
In the long scale, \(10^{903}\) is called quinquagintacentilliard.
In the modified Conway system, \(10^{312}\) in the short scale is also called trecentillion. Meauk pointed out that trecentillion has 2 meanings of \(10^{312}\) and \(10^{903}\) in the modified Conway system.[6] In the Conway's system, \(10^{312}\) is distinguished as trescentillion.
Decimal expansion[]
Written out in decimal form trecentillion (in the short scale) is:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
In long scale:
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Approximations[]
For the short scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{903}\) (exact) | |
Arrow notation | \(10\uparrow 903\) (exact) | |
Steinhaus-Moser Notation | 354[3] | 355[3] |
Chained arrow notation | \(10\rightarrow 903\) (exact) | |
Taro's multivariable Ackermann function | A(3,2996) | A(3,2997) |
BEAF & Bird's array notation | {10,903} (exact) | |
Hyper-E notation | E903 (exact) | |
s(n) map | \(s(1)^3(\lambda x.x+1)(8)\) | \(s(1)^3(\lambda x.x+1)(9)\) |
m(n) map | m(1)(354) | m(1)(355) |
Bashicu matrix system | (0)(0)(0)(0)(0)(0)(0)(0)(0)[58] | (0)(0)(0)(0)(0)(0)(0)(0)(0)[59] |
Copy notation | 9[903] | 10[452] |
Pound-Star Notation | #*((64))*18 | #*((65))*18 |
Hyperfactorial array notation | 413! | 414! |
Fast-growing hierarchy | \(f_2(2988)\) | \(f_2(2989)\) |
Hardy hierarchy | \(H_{\omega^2}(2988)\) | \(H_{\omega^2}(2989)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^2 9+3}}(10)\) (exact) |
For the long scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{1800}\) (exact) | |
Arrow notation | \(10\uparrow 1800\) (exact) | |
Steinhaus-Moser Notation | 641[3] | 642[3] |
Chained arrow notation | \(10\rightarrow 1800\) (exact) | |
Taro's multivariable Ackermann function | A(3,5976) | A(3,5977) |
BEAF & Bird's array notation | {10,1800} (exact) | |
Hyper-E notation | E1800 (exact) | |
s(n) map | \(s(1)^3(\lambda x.x+1)(9)\) | \(s(1)^3(\lambda x.x+1)(10)\) |
m(n) map | m(1)(641) | m(1)(642) |
Bashicu matrix system | (0)(1)[3] | (0)(1)[4] |
Copy notation | 9[1800] | 1[1801] |
Pound-Star Notation | #*((823))*24 | #*((824))*24 |
Hyperfactorial array notation | 738! | 739! |
Fast-growing hierarchy | \(f_2(5966)\) | \(f_2(5967)\) |
Hardy hierarchy | \(H_{\omega^2}(5966)\) | \(H_{\omega^2}(5967)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega^3+\omega^2 8}}(10)\) (exact) |
Sources[]
- ↑ Conway and Guy. (1995) "The book of Numbers" Copernicus
- ↑ Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-28.
- ↑ Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-28.
- ↑ Fish. Conway's zillion numbers. Retrieved 2023-02-28.
- ↑ Fish. Conway's illion converter - 10^903. Retrieved 2023-02-28.
- ↑ Meauk's tweet
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
1,000–1024: 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
Main article: -illion
300–309: trecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)310–319: decitrecentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
320–329: vigintitrecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
330–339: trigintatrecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
340–349: quadragintatrecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
350–359: quinquagintatrecentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
360–369: sexagintatrecentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
370–379: septuagintatrecentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
380–389: octogintatrecentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
390–399: nonagintatrecentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)