Googolillion

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Googolillion (or decitriotriacontillion) is an "-illionized" version of the googol, equal to \(10^{3\left(10^{100}\right)+3}\) in the American system. In the long scale of naming zillions, accepted in French and Germany, it is equal to 10^6×10100. It is equal to 1 followed by 3×googol+3 zeros. It is 3×10¹⁰⁰+4 digits long, and is slightly larger than a googolplex. It is the googolth -illion.

Writing down the full decimal expansion would take 3×10⁹⁴+1 books of 400 pages each, with 2,500 digits on each page (except for the first, which would have 2,501).

Names in -illion systems

According to Landon Curt Noll's The English name of a number, googolillion is also known as:

one decmilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliamilliatillion

Approximations

For short scale:

Notation	Lower bound	Upper bound
Arrow notation	\(1000\uparrow(1+10\uparrow100)\)
Down-arrow notation	\(50\downarrow\downarrow60\)	\(368\downarrow\downarrow40\)
Steinhaus-Moser Notation	56[3][3]	57[3][3]
Copy notation	2[2[101]]	3[3[101]]
H* function	H(10H(32))
Taro's multivariable Ackermann function	A(3,A(3,332))	A(3,A(3,333))
Pound-Star Notation	#*((1))*(8,1,8,3)*10	#*((1))*(8,5,3,5,4)*7
BEAF	{1000,1+{10,100}}
Hyper-E notation	E(3+3E100)
Bashicu matrix system	(0)(1)[18]	(0)(1)[19]
Hyperfactorial array notation	(69!)!	(70!)!
Fast-growing hierarchy	\(f_2(f_2(327))\)	\(f_2(f_2(328))\)
Hardy hierarchy	\(H_{\omega^22}(327)\)	\(H_{\omega^22}(328)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^{\omega^2}3+3}}(10)\)

For long scale:

Notation	Lower bound	Upper bound
Arrow notation	\((10\uparrow6)\uparrow(10\uparrow100)\)
Down-arrow notation	\(735\downarrow\downarrow36\)	\(892\downarrow\downarrow35\)
Steinhaus-Moser Notation	56[3][3]	57[3][3]
Copy notation	5[5[101]]	6[6[101]]
H* function	H(19H(32))	H(20H(32))
Taro's multivariable Ackermann function	A(3,A(3,333))	A(3,A(3,334))
Pound-Star Notation	#*((1))*(5,1,4,6,4)*7	#*((1))*(11,10,6,1)*11
BEAF	{{10,6},{10,100}}
Hyper-E notation	E(6E100)
Bashicu matrix system	(0)(1)[18]	(0)(1)[19]
Hyperfactorial array notation	(69!)!	(70!)!
Fast-growing hierarchy	\(f_2(f_2(328))\)	\(f_2(f_2(329))\)
Hardy hierarchy	\(H_{\omega^22}(328)\)	\(H_{\omega^22}(329)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^{\omega^2}6}}(10)\)

See also

• googol
• googo-
• googolilliard

Standard -illion numbers 10³ⁿ⁺³ (10⁶ⁿ)

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
1,000–10³⁰: 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