# Appendix:English numerals

## Contents

## Naming rules (short scale)[edit]

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[edit]

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[edit]

Optionally, a hyphen can combine the lower part, as in "six hundred forty-two". In British English, the word "and" is used to separate a multiplier from a number less than one hundred. Some speakers of North American English also insert "and", 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[edit]

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[edit]

### Single digits[edit]

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[edit]

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[edit]

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[edit]

### Short and long scale[edit]

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 | 10^{6} |
10^{6} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

milliard | 10^{9} |
✓ | ✓ | ✓ | ✓ | |||||

billion | 10^{9} |
10^{12} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * |

billiard | 10^{15} |
* | * | ✓ | ||||||

trillion | 10^{12} |
10^{18} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * |

trilliard | 10^{21} |
* | * | * | ✓ | |||||

quadrillion | 10^{15} |
10^{24} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

quintillion | 10^{18} |
10^{30} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

sextillion | 10^{21} |
10^{36} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

septillion | 10^{24} |
10^{42} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

octillion | 10^{27} |
10^{48} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

nonillion | 10^{30} |
10^{54} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

decillion | 10^{33} |
10^{60} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

undecillion | 10^{36} |
10^{66} |
✓ | ✓ | ✓ | * | ||||

duodecillion | 10^{39} |
10^{72} |
✓ | ✓ | ✓ | * | ||||

tredecillion | 10^{42} |
10^{78} |
✓ | ✓ | ✓ | * | ||||

quattuordecillion | 10^{45} |
10^{84} |
✓ | ✓ | ✓ | * | ||||

quindecillion (quinquadecillion) | 10^{48} |
10^{90} |
✓ | ✓ | ✓ | * | ||||

sexdecillion (sedecillion) | 10^{51} |
10^{96} |
✓ | ✓ | ✓ | * | ||||

septendecillion | 10^{54} |
10^{102} |
✓ | ✓ | ✓ | * | ||||

octodecillion | 10^{57} |
10^{108} |
✓ | ✓ | ✓ | * | ||||

novemdecillion (novendecillion) | 10^{60} |
10^{114} |
✓ | ✓ | ✓ | * | ||||

vigintillion | 10^{63} |
10^{120} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

googol | 10^{100} |
10^{100} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | * | |

centillion | 10^{303} |
10^{600} |
✓ | ✓ | ✓ | * | ||||

googolplex | 10^{10100} |
10^{10100} |
✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

### Usage notes[edit]

- 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. - The dictionary abbreviations are as follows :
**AHD4**—*the American Heritage Dictionary*, 4th edition, ISBN 0-395-82517-2. [1].**COD**— Cambridge Dictionaries Online, Cambridge, UK: Cambridge University Press.**OED2**—*Oxford English Dictionary*, 2nd edition, Oxford, UK: Oxford University Press. ISBN 0198611862 (and addendums since publication in 1989).**OEDnew**—*Oxford English Dictionary*, New Edition, Oxford, UK: Oxford University Press. [2] (subscription required), checked April 2007.**RHD2**—*The Random House Dictionary*, 2nd Unabridged Edition, 1987, Random House.**SOED3**—*Shorter Oxford English Dictionary*, 3rd edition, 1993, Oxford: Clarendon Press.**W3**—*Webster's Third New International Dictionary, Unabridged*, 1993, Merriam-Webster.**UM**—*How 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 10^{9}, which is what Americans call a billion.**billiard**unit of quantity equal to 10^{15}, 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 10^{21}, 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[edit]

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 | 10^{0} |
1 | one |

ten | 10 | 10^{1} |
10 | ten |

one hundred | 100 | 10^{2} |
100 | one hundred |

one thousand | 1,000 | 10^{3} |
1,000 | one thousand |

ten thousand | 10,000 | 10^{4} |
10,000 | ten thousand |

one lakh (also lac) | 1,00,000 | 10^{5} |
100,000 | one hundred thousand |

ten lakh | 10,00,000 | 10^{6} |
1,000,000 | one million |

one crore | 1,00,00,000 | 10^{7} |
10,000,000 | ten million |

ten crore | 10,00,00,000 | 10^{8} |
100,000,000 | one hundred million |

one arab / one hundred crore | 1,00,00,00,000 | 10^{9} |
1,000,000,000 | one billion |

one thousand crore / ten arab | 10,00,00,00,000 | 10^{10} |
10,000,000,000 | ten billion |

ten thousand crore / one kharab / one hundred arab | 1,00,00,00,00,000 | 10^{11} |
100,000,000,000 | one hundred billion |

one lakh crore / ten kharab / one thousand arab | 10,00,00,00,00,000 | 10^{12} |
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 | 10^{13} |
10,000,000,000,000 | ten trillion |

one crore crore / ten neel | 10,00,00,00,00,00,000 | 10^{14} |
100,000,000,000,000 | one hundred trillion |

one padm / one hundred neel / ten crore crore | 1,00,00,00,00,00,00,000 | 10^{15} |
1,000,000,000,000,000 | one quadrillion |

ten padm / one hundred crore crore | 10,00,00,00,00,00,00,000 | 10^{16} |
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 | 10^{17} |
100,000,000,000,000,000 | one hundred quadrillion |

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

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 |

4 | quattor | quadraginta | quadringenti |

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 . This can be written as 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 and interpreted as **one centivigintiseptillion**, noting that the e from septe has been ellided.

## Groups and multiplying words[edit]

Coefficient | Noun | Result |
---|---|---|

1 | single | singlet |

2 | double | doublet twin |

3 | triple | triplet |

4 | quadruple | quadruplet |

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[edit]

Greek-based prefixes:

- 1: mono-
- 2: di-
- 3: tri-
- 4: tetra-
- 5: penta-
- 6: hexa-
- 7: hepta-
- 8: octa-
- 9: ennea-
- 10: deca-
- 12: dodeca-
- 20: icosa-
- 30: triacontra-
- 100: hecta-

## Historical numerals[edit]

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

### Duodecimal (base 12)[edit]

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)[edit]

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 |

## See also[edit]

- Appendix:Roman numerals
- Category:English numbers
- Category:English cardinal numbers
- Category:English ordinal numbers