# Appendix:English numerals

## Ordered by numerical value

### Counting numbers

Cardinal number Ordinal number
0 zero zeroth
1 one first
2 two second
3 three third
4 four fourth
5 five fifth
6 six sixth
7 seven seventh
8 eight eighth
9 nine ninth
Cardinal number Ordinal number
10 ten tenth
11 eleven eleventh
12 twelve twelfth
13 thirteen thirteenth
14 fourteen fourteenth
15 fifteen fifteenth
16 sixteen sixteenth
17 seventeen seventeenth
18 eighteen eighteenth
19 nineteen nineteenth

### Multiples of ten

Cardinal number Ordinal number
10 ten tenth
20 twenty twentieth
30 thirty thirtieth
40 forty fortieth
50 fifty fiftieth
60 sixty sixtieth
70 seventy seventieth
80 eighty eightieth
90 ninety ninetieth
100 a hundred a hundredth
Cardinal number Ordinal number
100 hundred hundredth
1000 thousand thousandth
10000 ten thousand ten thousandth
100000 hundred thousand hundred thousandth
1000000 million millionth
Modern (US) System Older (EU) System
10^9 billion milliard
10^12 trillion billion

To name actual numbers from the above table the digits are grouped into threes, each group of three is named, and separated with decreasing powers of a thousand. The groups are named by writing the first digit, if it exists, then hundred and then the name of the multiple of ten twenty followed by the last digit three. The separators should be replaced from right to left with increasing powers of a thousand, million, billion… For example $123,456,789$ becomes one hundred and twenty three million four hundred and fifty six thousand seven hundred and eighty nine. Due to the impractical length of numbers such as this it is uncommon to find numbers given to more than a few degrees of precision in this form, more often they are simply written using Arabic numerals. It should also be noted that if any of the groups is zero, then it is not stated, and an "and" is only included for terms less than one hundred. For example one million and one, and one million one thousand and five are both correct.

## General rules for very large numbers

Depending on whether you are using the old European system of powers of a million, or the more current system of powers of a thousand, then the name of a number can be created by extracting the name of the power from this table and then adding -illion to the end. This method should be treated with caution and it is common to find slight spelling variations, normally to aid with the pronunciation of the resulting word. In most situations it is preferable to write numbers such as these using standard form instead of words.[1]

Units Tens Hundreds
1 un deci centi
2 duo viginti ducenti
3 tre triginta trecenti
5 quinqua quinquaginta quingenti
6 sex sexaginta sescenti
7 septe septuaginta septigenti
8 octo octoginta octingenti
9 novem nonaginta nongenti

For an example of how this might work consider $10^{762}$. This can be written as $1000^{254}$ using the modern system. This is then interpreted as ducenti-quinquaginta-quattor-illion using the above table. The hyphens are normally removed leaving one ducentiquinquagintaquattorillion. In the older system it would be written as $1000000^{127}$ and interpreted as one centivigintiseptillion, noting that the e from septe has been ellided.

## Ordered by name

Name Short scale
(modern)
Long scale
(dated)
Authorities
AHD4 COD OED2 OEDnew RHD2 SOED3 W3 UM
million 106 106 *
milliard   109
billion 109 1012 *
billiard   1015         *   *
trillion 1012 1018 *
trilliard   1021 *       *   *
quintillion 1018 1030 *
sextillion 1021 1036 *
septillion 1024 1042 *
octillion 1027 1048 *
nonillion 1030 1054 *
decillion 1033 1060 *
undecillion 1036 1066 *
duodecillion 1039 1072 *
tredecillion 1042 1078 *
quattuordecillion 1045 1084 *
sexdecillion (sedecillion) 1051 1096 *
septendecillion 1054 10102 *
octodecillion 1057 10108 *
novemdecillion (novendecillion) 1060 10114 *
vigintillion 1063 10120 *
googol 10100 10100 *
centillion 10303 10600 *
googolplex 1010100 1010100

### Usage notes

1. An asterisk (*) denotes that it has not been verified whether the term so marked is or is not mentioned in the specified work of reference.
2. The dictionary abbreviations are as follows :
• AHD4the American Heritage Dictionary, 4th edition, ISBN 0-395-82517-2. [1].
• CODCambridge Dictionaries Online, Cambridge, UK: Cambridge University Press.
• OED2Oxford English Dictionary, 2nd edition, Oxford, UK: Oxford University Press. ISBN 0198611862 (and addendums since publication in 1989).
• OEDnewOxford English Dictionary, New Edition, Oxford, UK: Oxford University Press. [2] (subscription required), checked April 2007.
• RHD2The Random House Dictionary, 2nd Unabridged Edition, 1987, Random House.
• SOED3Shorter Oxford English Dictionary, 3rd edition, 1993, Oxford: Clarendon Press.
• W3Webster's Third New International Dictionary, Unabridged, 1993, Merriam-Webster.
• UMHow Many? A Dictionary of Units of Measures, published by Russ Rowlett and the University of North Carolina at Chapel Hill, online, accessed 1 April 2007.
milliard[1] a unit of quantity equal to 109, which is what Americans call a billion.
billiard unit of quantity equal to 1015, which is one quadrillion in American terminology or 1000 billion in traditional British terminology. The name is coined to parallel milliard, which has long been a name for 1000 million.
trilliard a unit of quantity equal to 1021, which is one sextillion in American terminology or 1000 trillion in traditional British terminology. The name is coined to parallel milliard, which has long been a name for 1000 million.

## Greek-based prefixes

Greek-based prefixes:

## Historical numerals

Numbers from a base-12 number system, base-20 numbers, and other historical numbers.

Duodecimal (base-12):

 Number Word Mathematical formula 6 half dozen ½ × 12 12 dozen 12 13 baker's dozen 12 + 1 13 long dozen 12 + 1 72 half gross ½ × (12 × 12) 120 short gross 10 × 12 120 small gross 10 × 12 120 great hundred 12 × 10 120 long hundred 12 × 10 144 gross 12 × 12 156 long gross (12 + 1) × 12 1200 long thousand 12 × 100 1728 great gross 12 × 12 × 12

Vigesimal (base 20):

 Number Word Mathematical formula 20 score 20 40 twoscore 2 × 20 60 threescore 3 × 20 80 fourscore 4 × 20 100 fivescore 5 × 20 120 sixscore 6 × 20 140 sevenscore 7 × 20 160 eightscore 8 × 20 180 ninescore 9 × 20 200 tenscore 10 × 20