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Not to be confused with ducentillion.

duocentillion is equal to \(10^{309}\) in the short scale and \(10^{612}\) in the long scale by Conway and Guy's naming system[1][2][3][4] and with Jonathan Bowers system (short scale)[5] as it is the 102nd -illion number. It is the smallest -illion number not expressible in the double-precision floating-point format, as it maxes out at \(2^{1,024}\).

In the long scale, \(10^{309}\) is called unquinquagintilliard.

Aarex Tiaokhiao gave the name cetertillion, referring to the short-scale value of this number.[6]

Do not confuse this number with Landon Curt Noll's duocentillion which means \(10^{603}\) in the short scale or ducentillion in Conway's system.[7][8]

Decimal Expansion[]

1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Approximations[]

Notation Lower bound Upper bound
Scientific notation \(1\times10^{309}\)
Arrow notation \(10\uparrow309\)
Steinhaus-Moser Notation 143[3] 144[3]
Chained arrow notation \(10\rightarrow309\)
Copy notation 9[309] 10[155]
Taro's multivariable Ackermann function A(3,1023) A(3,1024)
Pound-Star Notation #*((608))*11 #*((609))*11
BEAF & Bird's array notation {10,309}
Hyper-E notation E309
Bashicu matrix system (0)(0)(0)(0)(0)(0)[67317] (0)(0)(0)(0)(0)(0)[67318]
Hyperfactorial array notation 170! 171!
Fast-growing hierarchy \(f_2(1\,016)\) \(f_2(1\,017)\)
Hardy hierarchy \(H_{\omega^2}(1\,016)\) \(H_{\omega^2}(1\,017)\)
Slow-growing hierarchy \(g_{\omega^{\omega^23+9}}(10)\)

Sources[]

See also[]

Main article: -illion
100–109: centillion (un- · duo- · tres- · quattuor- · quin- · sex- · septen- · octo- · noven-)
110–119: decicentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
120–129: viginticentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septem- · octo- · novem-)
130–139: trigintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
140–149: quadragintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
150–159: quinquagintacentillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
160–169: sexagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
170–179: septuagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
180–189: octogintacentillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
190–199: nonagintacentillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
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