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. These definitions are no longer used in English-speaking countries, but there are equivalents in other languages such as French and German.
Written out in decimal form billion (in the short scale) is:
In long scale:
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.
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
- ↑ Billion at Wolfram MathWorld
- ↑ Rowlett, Russ. Names for Large Numbers. Retrieved 2013-05-15.
- ↑ Aarex Tiaokhiao's illion numbers
- ↑ Part 1 (LAN) - Aarex Googology
- ↑ AAN Numbers - P1 - Aarex Googology
- ↑ Part 1 - My Large Numbers
- ↑ [1]
- ↑ 8.0 8.1 Saibian, Sbiis. 2.1.4 - Everyday Large Numbers for a Modern World. Retrieved 2013-05-15.
- ↑ https://en.wikipedia.org/wiki/List_of_most_viewed_YouTube_videos
See also
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
Megoogol · Meg-Googol · Meg-Doogol · Meg-Kiloogol · Meg-Kil-Googol · Meg-Dukiloogol · Meg-Trukiloogol · Dumegoogol · Dumeg-Googol · Dumeg-Kiloogol · Dumeg-Dukiloogol · Trumegoogol · Trumeg-Kiloogol · Tetrumegoogol · Pentumegoogol · Gigoogol · Gig-Googol · Gig-Kiloogol · Gig-Megoogol · Dugigoogol · Trugigoogol · Teroogol · Duteroogol · Truteroogol · Petoogol · Ectoogol · Zettoogol · Yottoogol · Xennoogol · Wekoogol
Note: The readers should be careful that numbers defined by Username5243's Array Notation are ill-defined as explained in Username5243's Array Notation#Issues. So, when an article refers to a number defined by the notation, it actually refers to an intended value, not an actual value itself (for example, a[c]b = \(a \uparrow^c b\) in arrow notation). In addition, even if the notation is ill-defined, a class category should be based on an intended value when listed, not an actual value itself, as it is not hard to fix all the issues from the original definition, hence it should not be removed.