Appendix:English numerals

This appendix discusses numbers or numerals in English generally. "Numerals" is also a grammatical part of speech, but only applies to certain types of numbers. (See #Parts of speech.)

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 multiples of 10, a multiple of ten is followed by a single digit number 1-9, and the value is the sum. For example, "42" is "forty-two", which places a numeral "4" before a numeral "2" to indicate that the 4 represents "forty", or 4 times 10. "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 multiples 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 and forty two" and "919" is "nine hundred and nineteen".

For larger numbers, each additional numeral at the beginning of the string generally represents another power of ten. Every additional (up to) three digits are grouped using the rules for numbers 1-999, then paired with a multiplier.

So with the multiplier "thousand" for example: 2,001 is "two thousand one" and 1,234 is "one thousand two hundred and thirty four".

One informal variant omits the use of the word thousand for example "fifteen hundred" instead of "one thousand five hundred". This variant tends to be used only in cases where it results in shorter pronunciation.

When writing in numerals, to aid comprehension these groups of three digits are typically separated—for example, with a comma in countries where the decimal mark is the period. (To be manipulated by machine, these separators are usually omitted. Lists/columns and tables of numbers may use spatial alignment in addition to or instead of commas.)

Similarly, when writing numbers with words, these groups are written using the rules for 1-999 followed by the multiplier. (Any group that is "000" is neither written in words nor pronounced.) Due to the impractical length, it is uncommon to find numbers with more than a few non-zero digits in words; more often they are simply written using . Examples:

375,000 has each numeral at the place in the string of numerals that represents its power of ten. Written fully in words ("three-hundred and seventy-five thousand"), the group "three-hundred and seventy-five" modifies the word "thousand".

Compare 3,750, for which each word representing a numeral is immediately modified by a word representing its power of ten: "three-thousand", "seven-hundred", "and" "fifty".

954,020,672: "nine hundred and fifty four million twenty thousand six hundred and seventy two" (uncommonly seen due to length)

20,000,000: "twenty million" (commonly seen due to brevity)

Ordinal numbers

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

first
second
third
fourth
twentieth
twenty-first (not twentieth first)

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 are appended to the numerals. For example:

1st
2nd
3rd
4th
20th
21st

Systematic variations

The words for numbers less than one hundred are varied as follows: Those not expressible by a single word can when written be joined by a hyphen, as in "six hundred forty-two". In British English, the word "and" is typically inserted before them. (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
six hundred and twenty-two 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".

In British English, the phrases "thousand million", "thousand billion", and "thousand trillion" are sometimes used in place of "billion", "trillion", and "quadrillion", respectively.

The determiners a or the can grammatically 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 1,984 is pronounced "nineteen eighty four"; referring to that year with the systematic reading "nineteen hundred and 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:

2,001: "two thousand and one" or rarely "twenty oh one"
2,015: "two thousand and fifteen" or very commonly "twenty fifteen"

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

Small whole numbers

Single digits

	Cardinal number	Ordinal number	Abbreviation of ordinal number
0	zero	zeroth	0th
1	one	first	1st
2	two	second	2nd
3	three	third	3rd
4	four	fourth	4th
5	five	fifth	5th
6	six	sixth	6th
7	seven	seventh	7th
8	eight	eighth	8th
9	nine	ninth	9th

Irregular numbers: 10-19

	Cardinal number	Ordinal number	Abbreviation of ordinal number
10	ten	tenth	10th
11	eleven	eleventh	11th
12	twelve	twelfth	12th
13	thirteen	thirteenth	13th
14	fourteen	fourteenth	14th
15	fifteen	fifteenth	15th
16	sixteen	sixteenth	16th
17	seventeen	seventeenth	17th
18	eighteen	eighteenth	18th
19	nineteen	nineteenth	19th

Multiples of ten

	Cardinal number	Ordinal number	Abbreviation of ordinal number
20	twenty	twentieth	20th
30	thirty	thirtieth	30th
40	forty	fortieth	40th
50	fifty	fiftieth	50th
60	sixty	sixtieth	60th
70	seventy	seventieth	70th
80	eighty	eightieth	80th
90	ninety	ninetieth	90th

Fractions

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Fraction (mathematics)

Common fractions

Common fractions are indicated by using the cardinal form for the numerator and the ordinal form for the denominator, with a few exceptions for small numbers. Fractions are typically but not always normalized to proper fractions or integers with proper fraction components.

Number	Regular form	Irregular form
1/1	(none; one first is incorrect and would be interpreted as an ordinal)	one whole
1/2	(none; one second is incorrect and would be interpreted as a measure of time, 1/60th of a minute)	one-half
1/3	one-third
2/3	two-thirds
1/4	one-fourth	one-quarter
2/4	two-fourths (but typically normalized to one half)	two-quarters
1/5	one-fifth
1/6	one-sixth
1/7	one-seventh
1/8	one-eighth
1/9	one-ninth
1/10	one-tenth
1/11	one-eleventh
1/12	one-twelfth
3/4	three-fourths	three-quarters
3/5	three-fifthss
3/8	three-eighths
4/5	four-fifths
7/8	seven-eighths

GPO manual states: "Print a hyphen between the elements of a fraction, but omit it between the numerator and the denominator when the hyphen appears in either or in both.

one-thousandth

two-thirds

two one-thousandths

twenty-three thirtieths

twenty-one thirty-seconds

three-fourths of an inch"

Decimal fractions

Decimal fractions are typically written as Hindu-Arabic numerals (like 0.125). When written as words, the symbols are generally translated one at a time, for example "zero point one two five". Zero or nought can also be written as oh, but this may be considered casual and is more common when being spoken.

Multiplying numbers

Short and long scale

	Cardinal number	Ordinal number	Abbreviation of ordinal number
100	hundred	hundredth	100th
1,000	thousand	thousandth	1,000th
10,000	ten thousand	ten-thousandth	10,000th
100,000	hundred thousand	hundred-thousandth	100,000th
1,000,000	million	millionth	1,000,000th

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

Name	Short scale (modern)	Long scale (dated)	Authorities
Name	Short scale (modern)	Long scale (dated)	AHD4	COD	OED2	OEDnew	RHD2	SOED3	W3	UM
million	10⁶	10⁶	✓	✓	✓		✓	✓	✓	*
milliard		10⁹	✓		✓		✓			✓
billion	10⁹	10¹²	✓	✓	✓	✓	✓	✓	✓	*
billiard		10¹⁵					*		*	✓
trillion	10¹²	10¹⁸	✓	✓	✓	✓	✓	✓	✓	*
trilliard		10²¹	*				*		*	✓
quadrillion	10¹⁵	10²⁴	✓		✓	✓	✓	✓	✓	*
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	✓				✓		✓	*
quindecillion	10⁴⁸	10⁹⁰	✓				✓		✓	*
sexdecillion	10⁵¹	10⁹⁶	✓				✓		✓	*
septendecillion	10⁵⁴	10¹⁰²	✓				✓		✓	*
octodecillion	10⁵⁷	10¹⁰⁸	✓				✓		✓	*
novemdecillion	10⁶⁰	10¹¹⁴	✓				✓		✓	*
vigintillion	10⁶³	10¹²⁰	✓		✓	✓	✓	✓	✓	*
googol	10¹⁰⁰	10¹⁰⁰	✓		✓	✓	✓	✓	✓	*
centillion	10³⁰³	10⁶⁰⁰	✓		✓	✓				*
googolplex	10^10¹⁰⁰	10^10¹⁰⁰	✓		✓	✓	✓	✓	✓

Usage notes

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. [1].
- COD — Cambridge Dictionaries Online, Cambridge, UK: Cambridge University Press.
- OED2 — Oxford English Dictionary, 2nd edition, Oxford, UK: Oxford University Press. →ISBN (and addenda 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 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,^{[notes 1]} 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 $10^{762}$ . 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 elided.

Groups and multiplying words

Number	1	2	3	4	5
Modifier	single	double / twofold	triple / threefold	quadruple / fourfold	quintuple / pentuple / fivefold
Whole	loner / singleton / monad	pair / couple / twosome / dyad	trio / threesome / triad / troika	foursome / tetrad	fivesome
Part	only one / singlet	twin / one of two / doublet	triplet / one of three	quadruplet / one of four	quintuplet / pentuplet / one of five
Number	6	7	8	9	10
Modifier	sextuple / hextuple / sixfold	septuple / heptuple / sevenfold	octuple / eightfold	ninefold / nonuple	tenfold / decuple
Whole	sixsome	sevensome	eightsome	ninesome	tensome / decad
Part	sextuplet / hextuplet / one of six	one of seven / septuplet / heptuplet	octuplet / one of eight	one of nine / nonuplet	one of ten / decuplet
Number	11	12	13	100	many
Modifier	elevenfold / undecuple / hendecuple	twelvefold / duodecuple	thirteenfold / tredecuple	a hundredfold / centuple	multiple
Whole	elevensome	twelvesome	thirteensome	hundredsome
Part	one of eleven / undecuplet / hendecuplet	one of twelve / duodecuplet	one of thirteen / tredecuplet	one of a hundred / centuplet	one of many / multiplet

Greek-based prefixes

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Numeral prefix

Greek-based prefixes:

1: mono-
2: di-
3: tri-
4: tetra-
5: penta-
6: hexa-
7: hepta-
8: octa-
9: ennea-
10: deca-
11: hendeca-
12: dodeca-
15: pentadeca-
20: icosa-
30: triaconta-
40: tetraconta-
50: pentaconta-
60: hexaconta-
70: heptaconta-
80: octaconta-
90: enneaconta-
100: hecta-
1,000: chilia-
10,000: myria-
1,000,000: mega-
1,000,000,000: giga-
1,000,000,000,000: tera-
1,000,000,000,000,000: peta-
1,000,000,000,000,000,000: exa-
1,000,000,000,000,000,000,000: zetta-
1,000,000,000,000,000,000,000,000: yotta-

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

Parts of speech

Cardinal numbers act as the part of speech known as "numerals". For example, in "two apples", "two" is a quantitative determiner (says how many there are) for the plural noun "apples".
Ordinal numbers act as adjectives. For example, "the second apple" specifies a property of a specific apple, which identifies its position or rank.
Fractional units act as nouns. For example, in "seven eighths", "seven" is a numeral that quantifies "eighths", a plural noun. Overall, this is a noun phrase. It can occur in predeterminer position ("she used only seven eighths the amount of flour called for by the recipe"), or with of in a partitive construction like "seven eighths of the apple".
Unlike true numerals, terms like hundred, million, dozen cannot function alone as determiners (*"hundred apples"). However, they can form a determiner when they follow a numeral ("thirty-one million", "two dozen"), or certain other determinatives ("the dozen apples", "several hundred apples"). These terms are most commonly classified as nouns, though some traditional grammars place them among adjectives.

Semantically, all these different parts of speech denote quantity or portion (albeit in different ways) and can be described as "numbers" (or numerals, as a synonym for numbers rather than as a grammatical part of speech).

Footnotes

Notes

↑ Especially for the 103-illion and the 300-illion, this method gives the same name of Trecentillion to them and causes the confusion.

References

↑ http://home.earthlink.net/~mrob/pub/math/largenum.html