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[[File:Billion.jpeg|thumb|Billion dollars visualised.]]
  
[[File:Billion.jpeg|thumb|Billion dollars visualised.]]
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A '''billion''' is equal to 10<sup>9</sup> = 1,000,000,000.<ref>[http://mathworld.wolfram.com/Billion.html Billion at Wolfram MathWorld]</ref> Like a [[million]], a billion is often used as an exaggeration to mean an indefinitely [[large number]].
 +
A '''billion''' is equal to 10<sup>9</sup> = 1,000<sup>3</sup> = 1,000,000,000.<ref>[http://mathworld.wolfram.com/Billion.html Billion at Wolfram MathWorld]</ref> Like a [[million]], a billion is often used as an exaggeration to mean an indefinitely [[large number]].
   
−
In the [[long scale]], 10<sup>9</sup> is called '''milliard''', whereas "billion" refers to 10<sup>12</sup>. These definitions are no longer used in English-speaking countries, but there are equivalents in other languages such as French and German.
 +
In the [[long scale]], 10<sup>9</sup> is called '''milliard''', whereas "billion" refers to 10<sup>12</sup> = 1,000,000,000,000. These definitions are no longer used in English-speaking countries, but there are equivalents in other languages such as French and German.
   
−
To prevent confusion with the similar sounding “million”, or with 10<sup>12</sup>, even some languages, such as {{w|Turkish language|Turkish}}, which otherwise use [[short scale]], use the term “milliard” (Turkish: “milyar”) for 10<sup>9</sup>.
 +
To prevent confusion with the similar sounding "million", or with 10<sup>12</sup>, even some languages, such as {{w|Turkish language|Turkish}}, which otherwise use [[short scale]], use the term "milliard" (Turkish: "milyar") for 10<sup>9</sup>.
   
 
Other names for this number are '''gillion'''<ref>{{cite web|first=Russ|last=Rowlett|title=Names for Large Numbers|url=http://www.unc.edu/~rowlett/units/large.html|accessdate=2013-05-15}}</ref> (from [[giga-]], in Rowlett's Greek-based system) and '''tretillion'''<ref>[https://sites.google.com/site/aarexnumbers/home/flo2i Aarex Tiaokhiao's illion numbers]</ref> (by [[Aarex Tiaokhiao]]).
  
Other names for this number are '''gillion'''<ref>{{cite web|first=Russ|last=Rowlett|title=Names for Large Numbers|url=http://www.unc.edu/~rowlett/units/large.html|accessdate=2013-05-15}}</ref> (from [[giga-]], in Rowlett's Greek-based system) and '''tretillion'''<ref>[https://sites.google.com/site/aarexnumbers/home/flo2i Aarex Tiaokhiao's illion numbers]</ref> (by [[Aarex Tiaokhiao]]).
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== Examples ==
  
== Examples ==
−
* One billion seconds is roughly 31.7 years, and billion minutes is close to two millenia. 12:32 AM, April 29, 1902 marked exactly one billion minutes from 1 A.D. <!-- There is no year zero. -->
 +
* One billion seconds is roughly 31.7 years, and billion minutes is nearly two millenia. 12:32 AM, April 29, 1902 marked exactly one billion minutes from 1 A.D. <!-- There is no year zero. -->
 
* The internet contains more than a billion webpages.<ref name="ELNfaMW">{{cite web|first=Sbiis|last=Saibian|authorlink=Sbiis Saibian|title=2.1.4 - Everyday Large Numbers for a Modern World|url=https://sites.google.com/site/largenumbers/home/2-1/everyday_large_numbers|accessdate=2013-05-15}}</ref>
  
* The internet contains more than a billion webpages.<ref name="ELNfaMW">{{cite web|first=Sbiis|last=Saibian|authorlink=Sbiis Saibian|title=2.1.4 - Everyday Large Numbers for a Modern World|url=https://sites.google.com/site/largenumbers/home/2-1/everyday_large_numbers|accessdate=2013-05-15}}</ref>
 
* It would take 951 years for a faucet running on full power to waste a billion gallons of water.<ref name="ELNfaMW" />
  
* It would take 951 years for a faucet running on full power to waste a billion gallons of water.<ref name="ELNfaMW" />
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Furthermore, it was also the prize for correctly answering the first six questions in the Turkish game show ''{{w|Kim 500 Milyar İster?}}'' in first {{w|Turkish lira}}.
  
Furthermore, it was also the prize for correctly answering the first six questions in the Turkish game show ''{{w|Kim 500 Milyar İster?}}'' in first {{w|Turkish lira}}.
  +
== Approximations ==
  +
For short scale:
  +
{| border="0" cellpadding="1" cellspacing="1" class="article-table"
  +
|-
  +
! scope="col"|Notation
  +
! scope="col"|Lower bound
  +
! scope="col"|Upper bound
  +
|-
  +
|[[Scientific notation]]
  +
|colspan="2" align="center"|\(1\times10^9\)
  +
|-
  +
|[[Arrow notation]]
  +
|colspan="2" align="center"|\(10\uparrow9\)
  +
|-
  +
|[[Steinhaus-Moser Notation]]
  +
|9[3]
  +
|10[3]
  +
|-
  +
|[[Copy notation]]
  +
|9[9]
  +
|10[5]
  +
|-
  +
|[[Taro's multivariable Ackermann function]]
  +
|A(3,26)
  +
|A(3,27)
  +
|-
  +
|[[Pound-Star Notation]]
  +
|#*(1,2,3)*3
  +
|#*(2,2,3)*3
  +
|-
  +
|[[BEAF]]
  +
|colspan="2" align="center"|{10,9}
  +
|-
  +
|[[Hyper-E notation]]
  +
|colspan="2" align="center"|E9
  +
|-
  +
|[[Bashicu matrix system]]
  +
|(0)[31622]
  +
|(0)[31623]
  +
|-
  +
|[[Hyperfactorial array notation]]
  +
|12!
  +
|13!
  +
|-
  +
|[[Fast-growing hierarchy]]
  +
|\(f_2(25)\)
  +
|\(f_2(26)\)
  +
|-
  +
|[[Hardy hierarchy]]
  +
|\(H_{\omega^2}(25)\)
  +
|\(H_{\omega^2}(26)\)
  +
|-
  +
|[[Slow-growing hierarchy]]
  +
|colspan="2" align="center"|\(g_{\omega^9}(10)\)
  +
|}
  +
  +
For long scale:
  +
{| border="0" cellpadding="1" cellspacing="1" class="article-table"
  +
|-
  +
! scope="col"|Notation
  +
! scope="col"|Lower bound
  +
! scope="col"|Upper bound
  +
|-
  +
|[[Scientific notation]]
  +
|colspan="2" align="center"|\(1\times10^{12}\)
  +
|-
  +
|[[Arrow notation]]
  +
|colspan="2" align="center"|\(10\uparrow12\)
  +
|-
  +
|[[Steinhaus-Moser Notation]]
  +
|11[3]
  +
|12[3]
  +
|-
  +
|[[Copy notation]]
  +
|9[12]
  +
|1[13]
  +
|-
  +
|[[Taro's multivariable Ackermann function]]
  +
|A(3,36)
  +
|A(3,37)
  +
|-
  +
|[[Pound-Star Notation]]
  +
|#*(4,2,3)*4
  +
|#*(1,2)*8
  +
|-
  +
|[[BEAF]]
  +
|colspan="2" align="center"|{10,12}
  +
|-
  +
|[[Hyper-E notation]]
  +
|colspan="2" align="center"|E12
  +
|-
  +
|[[Bashicu matrix system]]
  +
|colspan="2" align="center"|(0)(0)[1000]
  +
|-
  +
|[[Hyperfactorial array notation]]
  +
|14!
  +
|15!
  +
|-
  +
|[[Fast-growing hierarchy]]
  +
|\(f_2(34)\)
  +
|\(f_2(35)\)
  +
|-
  +
|[[Hardy hierarchy]]
  +
|\(H_{\omega^2}(34)\)
  +
|\(H_{\omega^2}(35)\)
  +
|-
  +
|[[Slow-growing hierarchy]]
  +
|colspan="2" align="center"|\(g_{\omega^{\omega+2}}(10)\)
  +
|}
   
 
== Sources ==
  
== Sources ==
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*[[Byllion]]
  
*[[Byllion]]
 
{{illion}}
  
{{illion}}
  +
−
{{Numbers by Username5243}}
  
 
[[de:Billion]]
  
[[de:Billion]]
  +
[[fr:Billion]]
 
[[nl:Biljoen]]
  
[[nl:Biljoen]]
 
[[cs:Bilión]]
  
[[cs:Bilión]]
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[[Category:Game show prizes]]
  
[[Category:Game show prizes]]
 
[[Category:Illion]]
  
[[Category:Illion]]
−
[[Category:Numbers with 10 to 21 digits]]
 +
[[Category:Numbers with 7 to 29 digits]]
 
[[Category:Powers of 10 with exponent not ending in a 0 or a 3]]
  
[[Category:Powers of 10 with exponent not ending in a 0 or a 3]]
  +
[[Category:Tier 1 -illion numbers]]
  +
[[Category:Googol Regiment]]

Revision as of 04:17, 23 December 2019

Billion

Billion dollars visualised.

A billion is equal to 109 = 1,0003 = 1,000,000,000.[1] Like a million, a billion is often used as an exaggeration to mean an indefinitely large number.

In the long scale, 109 is called milliard, whereas "billion" refers to 1012 = 1,000,000,000,000. These definitions are no longer used in English-speaking countries, but there are equivalents in other languages such as French and German.

To prevent confusion with the similar sounding "million", or with 1012, even some languages, such as Turkish, which otherwise use short scale, use the term "milliard" (Turkish: "milyar") for 109.

Other names for this number are gillion[2] (from giga-, in Rowlett's Greek-based system) and tretillion[3] (by Aarex Tiaokhiao).

Aarex Tiaokhiao calls this number noovol, 9-noogol[4], or goonaolheptault, and it's equal to a(10,100,0)x[7] in Aarex's Array Notation.[5]

Username5243 calls this number niloogolsextiplex or goonvol, and it's equal to 10[1]9 in Username5243's Array Notation.[6]

This number is called one arab in the Indian number system[7].

Examples

  • One billion seconds is roughly 31.7 years, and billion minutes is nearly two millenia. 12:32 AM, April 29, 1902 marked exactly one billion minutes from 1 A.D.
  • The internet contains more than a billion webpages.[8]
  • It would take 951 years for a faucet running on full power to waste a billion gallons of water.[8]
  • Gangnam Style, a hit single/music video by Korean rapper PSY, became the first YouTube video to reach 1 billion views in December 2012. It has nearly 3 billion views, and it held the former record of the video with the most views. The current record is Despacito with more than 4.14 billion views.[9]
  • The world population is around 7.5 billion.
  • The SI prefix giga- multiplies by one billion.
  • You could make 1,000 sand castles each containing a million grains of sand with 1 billion grains of sand.
  • The oldest billionaire of all time was Walter Haefner who died at the age of 101.

Currency-related use

Some currencies, such as the German Papiermark, the Hungarian pengő and the third Zimbabwean dollar, had banknotes with this number in the denomination.

It was also the prize for correctly answering all fifteen questions in the Italian game show Chi vuol essere miliardario? in Italian lire.

Furthermore, it was also the prize for correctly answering the first six questions in the Turkish game show Kim 500 Milyar İster? in first Turkish lira.

Approximations

For short scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^9\)
Arrow notation \(10\uparrow9\)
Steinhaus-Moser Notation 9[3] 10[3]
Copy notation 9[9] 10[5]
Taro's multivariable Ackermann function A(3,26) A(3,27)
Pound-Star Notation #*(1,2,3)*3 #*(2,2,3)*3
BEAF {10,9}
Hyper-E notation E9
Bashicu matrix system (0)[31622] (0)[31623]
Hyperfactorial array notation 12! 13!
Fast-growing hierarchy \(f_2(25)\) \(f_2(26)\)
Hardy hierarchy \(H_{\omega^2}(25)\) \(H_{\omega^2}(26)\)
Slow-growing hierarchy \(g_{\omega^9}(10)\)

For long scale:

Notation Lower bound Upper bound
Scientific notation \(1\times10^{12}\)
Arrow notation \(10\uparrow12\)
Steinhaus-Moser Notation 11[3] 12[3]
Copy notation 9[12] 1[13]
Taro's multivariable Ackermann function A(3,36) A(3,37)
Pound-Star Notation #*(4,2,3)*4 #*(1,2)*8
BEAF {10,12}
Hyper-E notation E12
Bashicu matrix system (0)(0)[1000]
Hyperfactorial array notation 14! 15!
Fast-growing hierarchy \(f_2(34)\) \(f_2(35)\)
Hardy hierarchy \(H_{\omega^2}(34)\) \(H_{\omega^2}(35)\)
Slow-growing hierarchy \(g_{\omega^{\omega+2}}(10)\)

Sources

  1. ↑ Billion at Wolfram MathWorld
  2. ↑ Rowlett, Russ. Names for Large Numbers. Retrieved 2013-05-15.
  3. ↑ Aarex Tiaokhiao's illion numbers
  4. ↑ Part 1 (LAN) - Aarex Googology
  5. ↑ AAN Numbers - P1 - Aarex Googology
  6. ↑ Part 1 - My Large Numbers
  7. ↑ [1]
  8. ↑ 8.0 8.1 Saibian, Sbiis. 2.1.4 - Everyday Large Numbers for a Modern World. Retrieved 2013-05-15.
  9. ↑ https://en.wikipedia.org/wiki/List_of_most_viewed_YouTube_videos

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
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