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− | A '''tredecillion''' or '''septilliad'''<ref>[https://sites.google.com/site/largenumbers/home/appendix/a/numbers Sbiis Saibian's Ultimate Finite Numbers List Part I]</ref> is equal to 10<sup>42</sup> in |
+ | A '''tredecillion''' or '''septilliad'''<ref>[https://sites.google.com/site/largenumbers/home/appendix/a/numbers Sbiis Saibian's Ultimate Finite Numbers List Part I]</ref> is equal to 10<sup>42</sup> in [[short scale]], or 10<sup>78</sup> in [[long scale]].<ref>[http://mathworld.wolfram.com/Tredecillion.html Tredecillion at Wolfram MathWorld]</ref> |
In the [[long scale]], 10<sup>42</sup> is called [[septillion]], which is commonly used in France and Germany. |
In the [[long scale]], 10<sup>42</sup> is called [[septillion]], which is commonly used in France and Germany. |
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[[Aarex Tiaokhiao]] gave the name '''tetrecillion''', referring to the value of this number.<ref>[https://sites.google.com/site/aarexnumbers/home/flo2i Aarex Tiaokhiao's illion numbers]</ref> |
[[Aarex Tiaokhiao]] gave the name '''tetrecillion''', referring to the value of this number.<ref>[https://sites.google.com/site/aarexnumbers/home/flo2i Aarex Tiaokhiao's illion numbers]</ref> |
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+ | It is 43 digits long in short scale, and 79 digits long in long scale. |
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== Decimal expansion == |
== Decimal expansion == |
Revision as of 12:06, 26 March 2020
A tredecillion or septilliad[1] is equal to 1042 in short scale, or 1078 in long scale.[2]
In the long scale, 1042 is called septillion, which is commonly used in France and Germany.
This number is also called tetradekillion in Russ Rowlett's Greek-based naming system.[3]
Aarex Tiaokhiao gave the name tetrecillion, referring to the value of this number.[4]
It is 43 digits long in short scale, and 79 digits long in long scale.
Decimal expansion
- 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000 - short scale
- 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 - long scale
Examples
- There is about 100 tredecillion grams of matter contained in the grand total of all the stars in the Milky Way Galaxy.
- There are about 200 tredecillion atoms contained in the entire atmosphere of the Earth[5]
- The prefix tenatera- multiplies by one tredecillion.
Approximations
For short scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{42}\) | |
Arrow notation | \(10\uparrow42\) | |
Steinhaus-Moser Notation | 28[3] | 29[3] |
Copy notation | 9[42] | 1[43] |
Taro's multivariable Ackermann function | A(3,136) | A(3,137) |
Pound-Star Notation | #*(7,6,6,0,4)*6 | #*(8,6,6,0,4)*6 |
BEAF | {10,42} | |
Hyper-E notation | E42 | |
Bashicu matrix system | (0)(0)(0)(0)[421] | (0)(0)(0)(0)[422] |
Hyperfactorial array notation | 36! | 37! |
Fast-growing hierarchy | \(f_2(132)\) | \(f_2(133)\) |
Hardy hierarchy | \(H_{\omega^2}(132)\) | \(H_{\omega^2}(133)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega4+2}}(10)\) |
For long scale:
Notation | Lower bound | Upper bound |
---|---|---|
Scientific notation | \(1\times10^{78}\) | |
Arrow notation | \(10\uparrow78\) | |
Steinhaus-Moser Notation | 46[3] | 47[3] |
Copy notation | 9[78] | 1[79] |
Taro's multivariable Ackermann function | A(3,256) | A(3,257) |
Pound-Star Notation | #*(9,2,9,0,5,1,1)*7 | #*(10,2,9,0,5,1,1)*7 |
BEAF | {10,78} | |
Hyper-E notation | E78 | |
Bashicu matrix system | (0)(0)(0)(0)[74989] | (0)(0)(0)(0)[74990] |
Hyperfactorial array notation | 57! | 58! |
Fast-growing hierarchy | \(f_2(251)\) | \(f_2(252)\) |
Hardy hierarchy | \(H_{\omega^2}(251)\) | \(H_{\omega^2}(252)\) |
Slow-growing hierarchy | \(g_{\omega^{\omega7+8}}(10)\) |
List of prefixed numbers derived from decillion
Name | Short scale | Long scale |
---|---|---|
undecillion | 1036 | 1066 |
duodecillion | 1039 | 1072 |
tredecillion | 1042 | 1078 |
quattuordecillion | 1045 | 1084 |
quindecillion | 1048 | 1090 |
sexdecillion | 1051 | 1096 |
septendecillion | 1054 | 10102 |
octodecillion | 1057 | 10108 |
novemdecillion | 1060 | 10114 |
Sources
See also
- tredecyllion
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