-illion

> "*Although we value [your] donations, we were somewhat surprised to note that none of them ended in "-illion."*"
> ― Stephen Colbert[[source]]
>
>

The **-illion** system is a suffix used to represent the powers of ten, the only large number system that is widely in use except for systems in eastern Asia which are based on a myriad. It has two distinct forms, the **long scale** (based on Powers of a million) and the **short scale**. English predominantly uses the short scale, while other languages such as French and German use the long scale. The long scale was also used in UK English until 1974, when the British usage and the American usage became identical.

The short scale goes as follows:

* million =

10
6

{\displaystyle 10^6}
* billion =

10
9

{\displaystyle 10^9}
* trillion =

10

12

{\displaystyle 10^{12}}
* quadrillion =

10

15

{\displaystyle 10^{15}}
* quintillion =

10

18

{\displaystyle 10^{18}}
* sextillion =

10

21

{\displaystyle 10^{21}}
* *n*-illion = \(10^{(3n + 3)}\) using Latin prefix *n*

The long scale goes as follows:

* million = \(10^6\)
* milliard = \(10^9\)
* billion = \(10^{12}\)
* billiard = \(10^{15}\)
* trillion = \(10^{18}\)
* trilliard = \(10^{21}\)
* quadrillion = \(10^{24}\)
* quadrilliard = \(10^{27}\)
* *n*-illion = \(10^{6n}\)
* *n*-illiard = \(10^{(6n + 3)}\)

## In googological notations

For the short scale:

f
2

(

f
1
3

(
n
)
)

{\displaystyle f\_2(f\_1^3(n))}

 and

f
2

(

f
1
4

(
n
)
)

{\displaystyle f\_2(f\_1^4(n))}
 Slow-growing hierarchy | \(g\_{\omega^{n+1}}(1,000)\); just below \(g\_{\omega^\omega}(n)\)

For the long scale:

f
2

(

f
1
4

(
n
)
)

{\displaystyle f\_2(f\_1^4(n))}

 and

f
2

(

f
1
5

(
n
)
)

{\displaystyle f\_2(f\_1^5(n))}
 Slow-growing hierarchy | \(g\_{\omega^{2n}}(1,000)\); just below \(g\_{\omega^\omega}(n)\)

For -illiard:

 Slow-growing hierarchy | \(g\_{\omega^{2n+1}}(1,000)\); just below \(g\_{\omega^\omega}(n)\)

## See also

* millillion
* googolillion
* zillion
* Long and short scales on Wikipedia

**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 · trevigint · quattuorvigint · quinvigint · sexvigint · septenvigint · octovigint · novemvigint
**30–39:** trigintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**40–49:** quadragintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**50–59:** quinquagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**60–69:** sexagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**70–79:** septuagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**80–89:** octogintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**90–99:** nonagintillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**100–109:** centillion · un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-
**110–119:** decicentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**120–129:** viginticentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**130–139:** trigintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**140–149:** quadragintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**150–159:** quinquagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**160–169:** sexagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**170–179:** septuagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**180–189:** octogintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**190–199:** nonagintacentillion (un- · duo- · tre- · quattuor- · quin- · sex- · septen- · octo- · novem-)
**200–900:** ducent · trecent · duotrigintatrecent · quadringent · quingent · sescent · septuagintisescent · septingent · octingent · nongent
**1,000–1024:** millillion · dumill · trimill · quadrimill · quadrimilliquattuordecicent · quinmill · sexmill · septimill · octimill · nonimill · myr · undecimill · duodecimill · dumyr · trimyr · quadrimyr · quinmyr · sexmyr · septimyr · octimyr · nonimyr · centimill · ducentimill · trecentimill · quadringentimill · quingentimill · sescentimill · septingentimill · octingentmill · nongentimill · micr · nan · pic · femt · att · zept · yoct

(above template chooses Bowers coinages in later categories)