# Appendix:English numerals

## Naming rules (short scale)

English generally uses a decimal counting system for natural numbers. The names of the cardinal and ordinal numbers can be constructed from the below tables and a set of combining rules.

Each of the numbers specifically listed has a literal name that can be used on its own.

• To name numbers 21 through 99 that are not powers of 10, a power of ten is followed by a single digit number 1-9, and the value is the sum. For example, "42" is "forty two". "Zero" never combines with other numbers in the naming system, it is only pronounced in the name for 0.
• To name numbers 101 through 999 that are not powers of 100, the name of a digit 1-9 is followed by "hundred" (the individual values are multiplied together) to express the first digit, and the rules for smaller numbers are used for the remainder (the values of the hundreds part and the remainder are summed). For example, "642" is "six hundred forty two" and "919" is "nine hundred nineteen".
• For larger numbers, every group of additional three digits is written using the rules for numbers 1-999 and pair with the name of a multiplier. In countries where the decimal mark is the period, commas are generally used to separate the groups of three digits, to aid in reading. (These commas are usually omitted in situations where the numbers would be manipulated in a calculation.) A group of three digits that is 000 is not pronounced. So for example: 2,001 is "two thousand one" and 1234 is "one thousand two hundred thirty four".
Due to the impractical length of numbers such as this it is uncommon to find numbers with more than a few non-zero digits in this form; more often they are simply written using Arabic numerals. Examples:
• 954,020,672: "nine hundred fifty four million twenty thousand six hundred seventy two" (uncommonly seen due to length)
• 20,000,000: "twenty million" (commonly seen due to brevity)

### Ordinal numbers

When constructing names for oridinal numbers, the ordinal variant given in the charts below is only used for the final word. For example:

• fifth
• twentieth
• twenty fourth (not twentieth fourth)

Ordinal numbers can also be written with Arabic numerals, in which case the last two letters of what would be the final word in the written-out form is appended to the numerals. For example:

• 1st
• 2nd
• 3rd
• 4th
• 20th
• 21st

### Systematic variations

Optionally, a hypen can combine the lower part, as in "six hundred forty-two". Some speakers prefer to use the word "and" to separate a multiplier from a number less than one hundred, especially when the number is below 20. Examples:

• six hundred and two (instead of "six hundred two")
• six hundred and forty-two
• two thousand and one
• one thousand two hundred and thirty-four
• one million and one
• one million one thousand and five

As shown on the charts below, there are two systems for the names of multipliers, known as the "long system" and "short system", though the short system is generally now preferred in English, to avoid confusion.

In countries where the comma or middle dot is used as the decimal mark, spaces or periods are used for thousands separators. Some style guides prefer no digits separator for four-digit numbers (1000-9999).

In less formal speech, the names for the numbers 11-99 (except powers of ten) can be combined with "hundred" as an alternative to a longer systematic name using both "thousand" and "hundred". For example "eleven hundred" can replace "one thousand one hundred" but "twenty hundred and two" never replaces "two thousand and two" except poetically.

For large round numbers, familiar multipliers are sometimes repeated instead of using less familiar multipliers. For example, "one billion billion" instead of "one quintillion".

### Substitutions

The determiners a or the can gramattically substitute for "one", as in "a hundred" or "the first thousand"; and "a couple" can be used to mean two (though to some speakers "a couple" means "a few" which could perhaps range from two to five or higher).

The names of non-counting numbers - like in a code or a sequence or a naming scheme as for years or addresses - typically use a form of the "hundreds replace thousands" variation that also drops the "hundreds". Years and addresses are never written with commas as digit separators. For example, the year 1984 is pronounced "nineteen eighty four"; referring to that year with the systematic reading "nineteen hundred eighty four" sounds old-fashioned. Sequence numbers with zero digits have additional variations. More commonly than not, a zero in only the tens place is read as "oh" (as in the letter o), like "nineteen oh four". A zero in the hundreds place triggers use of the systematic name or the "hundreds replacement" variant. Examples:

• 2001: "two thousand one" or rarely "twenty oh one"
• 2015: "two thousand fifteen" or very commonly "twenty fifteen"

One complete variation for such non-counting numbers is to read individual digits. Informally, "oh" can once again substitude for zero in this scheme. For example, "1024" could be read "one zero two four" or "one oh two four".

## Small numbers

### Single digits

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

### Irregular numbers: 10-19

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
20 twenty twentieth
30 thirty thirtieth
40 forty fortieth
50 fifty fiftieth
60 sixty sixtieth
70 seventy seventieth
80 eighty eightieth
90 ninety ninetieth

## Multiplying numbers

### Short and long scale

Cardinal number Ordinal number
100 hundred hundredth
1000 thousand thousandth
10000 ten thousand ten thousandth
100000 hundred thousand hundred thousandth
1000000 million millionth

For higher multiplying terms, the ordinal suffix is always "th".

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.

### South Asian numbering system

In South Asian varieties of English, the traditional South Asian numbering system is commonly used instead of or alongside the short and long scale. This groups higher digits in pairs instead of triplets.

South Asian English Indian figure Power notation Arabic figure Short scale English
one 1 100 1 one
ten 10 101 10 ten
one hundred 100 102 100 one hundred
one thousand 1,000 103 1,000 one thousand
ten thousand 10,000 104 10,000 ten thousand
one lakh (also lac) 1,00,000 105 100,000 one hundred thousand
ten lakh 10,00,000 106 1,000,000 one million
one crore 1,00,00,000 107 10,000,000 ten million
ten crore 10,00,00,000 108 100,000,000 one hundred million
one arab / one hundred crore 1,00,00,00,000 109 1,000,000,000 one billion
one thousand crore / ten arab 10,00,00,00,000 1010 10,000,000,000 ten billion
ten thousand crore / one kharab / one hundred arab 1,00,00,00,00,000 1011 100,000,000,000 one hundred billion
one lakh crore / ten kharab / one thousand arab 10,00,00,00,00,000 1012 1,000,000,000,000 one trillion
ten lakh crore / one neel / one hundred kharab / ten thousand arab 1,00,00,00,00,00,000 1013 10,000,000,000,000 ten trillion
one crore crore / ten neel 10,00,00,00,00,00,000 1014 100,000,000,000,000 one hundred trillion
one padm / one hundred neel / ten crore crore 1,00,00,00,00,00,00,000 1015 1,000,000,000,000,000 one quadrillion
ten padm / one hundred crore crore 10,00,00,00,00,00,00,000 1016 10,000,000,000,000,000 ten quadrillion
one shankh / one hundred padm / one thousand crore crore / one lakh lakh crore 1,00,00,00,00,00,00,00,000 1017 100,000,000,000,000,000 one hundred quadrillion

## General rules for very large numbers (short and long scale)

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.

## Groups and multiplying words

Coefficient Noun Result
1 single singlet
2 double doublet
twin
3 triple triplet
5 quintuple
pentuple
quintuplet
pentuplet
6 sextuple
hextuple
sextuplet
hextuplet
7 heptuple heptuplet
8 octuple octuplet
9 nonuple nonuplet
10 decuple decuplet
11 undecuple
hendecuple
undecuplet
hendecuplet
12 duodecuple duodecuplet
13 tredecuple tredecuplet
100 centuple centuplet
many multiple multiplet

## 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