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 .)

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 Arabic numerals. 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".

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.

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.

Short and long scale
For higher multiplying terms, the ordinal suffix is always "th".

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:
 * AHD4 &mdash; the American Heritage Dictionary, 4th edition, ISBN 0-395-82517-2..
 * COD &mdash; Cambridge Dictionaries Online, Cambridge, UK: Cambridge University Press.
 * OED2 &mdash; Oxford English Dictionary, 2nd edition, Oxford, UK: Oxford University Press. ISBN 0198611862 (and addenda since publication in 1989).
 * OEDnew &mdash; Oxford English Dictionary, New Edition, Oxford, UK: Oxford University Press. (subscription required), checked April 2007.
 * RHD2 &mdash; The Random House Dictionary, 2nd Unabridged Edition, 1987, Random House.
 * SOED3 &mdash; Shorter Oxford English Dictionary, 3rd edition, 1993, Oxford: Clarendon Press.
 * W3 &mdash; Webster's Third New International Dictionary, Unabridged, 1993, Merriam-Webster.
 * UM &mdash; 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.

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.

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.

Greek-based prefixes
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-
 * 1,000,000,000,000,000,000,000,000,000: ronna-
 * 1,000,000,000,000,000,000,000,000,000,000: quetta-

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

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, , and 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).