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Not to be confused with trescentillion.

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[]

  1. Conway and Guy. (1995) "The book of Numbers" Copernicus
  2. Munafo, Robert. The Conway-Wechsler System. Retrieved 2023-02-28.
  3. Olsen, Steve. Big-Ass Numbers. Retrieved 2023-02-28.
  4. Fish. Conway's zillion numbers. Retrieved 2023-02-28.
  5. Fish. Conway's illion converter - 10^903. Retrieved 2023-02-28.
  6. Meauk's tweet

See also[]

Main article: -illion
1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non
10–19: 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-)
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