Appendix:Latin cardinal numerals
Cardinal numerals 
When someone counts items, that person uses cardinal values. In grammatical terms, a cardinal numeral is a word used to represent such a countable quantity. The English words one, two, three, four, etc. are all examples of cardinal numerals.
In Latin, most cardinal numerals behave as indeclinable adjectives. They are usually associated with a noun that is counted, but do not change their endings to agree grammatically with that noun. The exceptions are ūnus (“one”), duo (“two”), trēs (“three”), and multiples of centum (“hundred”), all of which decline. Additionally, although mīlle (“thousand”) is an indeclinable adjective in the singular, it becomes a declinable noun in the plural. These exceptions are further explained in later sections.
Summary table 
|1||I||ūnus, ūna, ūnum||11||XI||ūndecim||10||X||decem||100||C||centum|
|2||II||duo, duae, duo||12||XII||duodecim||20||XX||vīgintī||200||CC||ducentī, -ae, -a|
|3||III||trēs, tria||13||XIII||tredecim||30||XXX||trīgintā||300||CCC||trecentī, -ae, -a|
|4||IV||quattuor||14||XIV||quattuordecim||40||XL||quadrāgintā||400||CD||quadringentī, -ae, -a|
|5||V||quīnque||15||XV||quīndecim||50||L||quīnquāgintā||500||D||quīngentī, -ae, -a|
|6||VI||sex||16||XVI||sēdecim||60||LX||sexāgintā||600||DC||sescentī, -ae, -a|
|7||VII||septem||17||XVII||septendecim||70||LXX||septuāgintā||700||DCC||septingentī, -ae, -a|
|8||VIII||octō||18||XVIII||duodēvīgintī||80||LXXX||octōgintā||800||DCCC||octingentī, -ae, -a|
|9||IX||novem||19||XIX||ūndēvīgintī||90||XC||nōnāgintā||900||CM||nōngentī, -ae, -a|
Smaller cardinals 
The smaller cardinal numerals, from ūnus (“one”) to vīgintī (“twenty”), have spellings and forms that are not easily predictable and therefore must be learned by students of Latin. Larger cardinal numerals follow more regular patterns of assembly.
Inflection : The Latin ūnus (“one”) inflects like an irregular first and second declension adjective. The irregularities occur in the singular genitive, which ends in -īus instead of the usual -ī or -ae, and in the singular dative, which ends in -ī instead of the usual -ō or -ae.
The choice of ending will agree with the gender of the associated noun: ūnus equus ("one horse"), ūna clāvis ("one key"), ūnum saxum ("one stone"). The ending will also agree with the grammatical case of the associated noun: ūnīus equī (genitive), ūnam clāvem (accusative), ūnī saxō (dative).
Plural : Although it may seem strange at first sight, ūnus does have a set of plural forms. These forms are used when the associated noun has a plural form, but an inherently singular meaning. For example, the Latin noun castra (“camp”) occurs only as a plural neuter form and takes plural endings, even though it identifies one object, hence: ūnōrum castrōrum ("of one camp").
Compounds : When ūnus is used to form compound numerals, such as ūnus et vīgintī ("twenty-one"), the masculine nominative singular is used, and does not inflect. Unlike duo and trēs, the word ūnus is almost never used with mīlle (“thousand”) to indicate how many thousand.
|acc||duōs / duo||duās||duo|
Inflection : The Latin duo (“two”) has a highly irregular inflection. While some of the endings resemble those of a first and second declension adjective, others resemble those of a third declension adjective. In fact, its dative and ablative endings occur in no other Latin word. This is a remnant of an earlier dual form present in anteclassical Latin.
The choice of ending will agree with the gender of the associated noun, which will necessarily be plural: duo equī ("two horses"), duae clāvēs ("two keys"), duo saxa ("two stones"). The ending will also agree with the grammatical case of the associated noun: duōs equōs (accusative), duārum clāvum (genitive), duōbus saxīs (dative).
Compounds : When duo is used to form compound numerals, such as duo et vīgintī or vīgintī duo ("twenty-two"), the masculine nominative singular is used, and does not inflect. However, duo does inflect when used with the plural of mīlle (“thousand”) to indicate how many thousands: duo mīlia ("two thousands"), duōrum mīlium ("of two thousands").
The choice of ending will agree with the gender of the associated noun, which will necessarily be plural: trēs equī ("three horses"), trēs clāvēs ("three keys"), tria saxa ("three stones"). The ending will also agree with the grammatical case of the associated noun: trēs equōs (accusative), trium clāvum (genitive), tribus saxīs (dative).
Compounds : When trēs is used to form compound numerals, such as trēs et vīgintī or vīgintī trēs ("twenty-three"), the masculine nominative singular is used, and does not inflect. However, trēs does inflect when used with the plural of mīlle (“thousand”) to indicate how many thousands: tria mīlia ("three thousands"), trium mīlium ("of three thousands").
IV to XX 
|1||I||ūnus, ūna, ūnum||11||XI||ūndecim|
|2||II||duo, duae, duo||12||XII||duodecim|
Many of these numerals are mirrored in English words (such as quadrangle, quintuplet, sextuple, octopus). The numerals for 7 through 10 appear in the English names of months (September, October, November, and December). These months were the seventh through tenth of the Roman calendar, since the Roman year began with mārtius (“March”).
Teens : Latin cardinals larger than decem (“ten”) but less than vīgintī (“twenty”) are constructed by addition. The ending -decim (a form of decem) is attached to the numerals ūnūs through novem. The resultant compound carries the same value as the mathematical sum of the components. For example quattuordecim (“fourteen”) is quattuor (“four”) + decem (“ten”). English does much the same by attaching -teen (a form of ten) to smaller numerals, such as the numeral fourteen which is four + ten.
In some of these compounds, a spelling and pronunciation change occurs during the attachment, so that sex + decem drops the -x and lengthens the e to yield sēdecim. This kind of change also occurs in English, as in five + ten which softens the sound of the v and drops the e to yield fifteen.
Exceptions : There are two exceptions to the general pattern for forming the teens. In Classical Latin, the numerals for 18 and 19 are more frequently written as subtractive compounds. So, although 18 may be written as octōdecim, it is more often written as duodēvīgintī (literally "two from twenty"). Likewise, the numeral for 19 may be written as novemdecim, but is more often encountered as ūndēvīgintī (“one from twenty”).
For more information about the subtractive pattern of construction, see the section on "counting backwards".
Larger cardinals 
|Multiples of ten|
|Multiples of one hundred|
|100||C||centum 1||600||DC||sescentī, -ae, -a|
|200||CC||ducentī, -ae, -a||700||DCC||septingentī, -ae, -a|
|300||CCC||trecentī, -ae, -a||800||DCCC||octingentī, -ae, -a|
|400||CD||quadringentī, -ae, -a||900||CM||nōngentī, -ae, -a|
|500||D||quīngentī, -ae, -a||1000||M||mīlle, mīlia 2|
|1 centum does not inflect.
2 see the following section on mīlle.
|C (adj.)||NN (noun)|
The Latin mīlle (“thousand”) is irregular in that it has two forms. In the singular, it is an indeclinable adjective, but in the plural it is a noun that declines like a third declension neuter i-stem. Notice that the genitive plural ending is -ium.
Singular : In the singular, mīlle (“thousand”) functions as an adjective. This singular form is indeclinable, so its ending will remain the same rather than agree with the case or gender of the associated noun. However, the associated noun will necessarily be plural: mīlle equī ("thousand horses"), mīlle clāvēs ("thousand keys"), mīlle saxa ("thousand stones"). This is true regardless of the case or gender of the associated noun.
Plural : In the plural, mīlia functions as a noun, and will inflect according to how it is used in the sentence (subject, direct object, etc.). The associated noun being counted will necessarily be in the genitive plural, and so will not agree with the grammatical case of mīlia. Note that, if the numeral before mīlia is duo or trēs, then it will take a neuter form in the same grammatical case as mīlia : octō mīlia equōrum (nominative, "eight thousand of horses"), cum tribus mīlibus clāvum (ablative, "with three thousand of keys"), duōrum mīlium saxōrum (genitive, "of two thousand of stones").
Compound cardinals 
Latin cardinal numerals larger than vīgintī (“twenty”), that are not multiples of ten, are assembled as compound words. The components of these compounds are the numerals ūnus (“one”) through novem (“nine”) and the multiples of decem (“10”), the multiples of centum (“100”), and mīlle (“1000”).
Compound numerals in Latin are assembled by one of two basic methods: additive or subtractive. Most compound numerals are additive, meaning that the value of the compound numeral is calculated by adding the values of the component words. However, a few Latin compound numerals are subtractive, meaning that the value of the compound numeral is calculated by subtracting the values of the component words. A large-valued compound numeral may incorporate both additive and subtractive components.
Additive compounds 
Counting backwards 
|Tens +8 ( or –2 )||Tens +9 ( or –1 )|
Of the Latin compound numerals less than centum (“100”), seventeen are normally subtractive. All of these special cases represent values that are one or two less than a multiple of ten, and have names that subtract from a starting value rather than adding to that value. These seventeen exceptions are displayed in the table at right. Note that the compound numeral for 98 is not among the special cases, but instead is formed in the usual additive way. Subtractive compounds normally are written as single words (with no spaces) and are indeclinable.
Numerals representing cardinal values that are eight more (two less) than a multiple of ten are constructed literally as:
Thus, the numeral for 38 is normally written as duodēquadrāgintā (“two from forty”), rather than as the expected trīgintā octō (“thirty-eight”) or octō et trīgintā (“eight and thirty”). The latter two additive forms are possible, but are not found in Classical Latin as frequently as the subtractive form.
Numerals representing cardinal values that are nine more (one less) than a multiple of ten are constructed literally as:
Thus, the numeral for 39 is normally written as ūndēquadrāgintā (“one from forty”), rather than as the expected trīgintā novem (“thirty-nine”) or novem et trīgintā (“nine and thirty”). The latter two additive forms are possible, but are not found in Classical Latin as frequently as the subtractive form.
Numbers are almost always treated as adjectives, and often come before the noun. They may be used alone as substantive nouns, but as most are indeclinable, this tends to be ambiguous. Mille behaves differently; in the plural, as milia, the noun being counted must be in the genitive plural. For example, "two thousand soldiers" would be "duo milia militum" (literally, "two thousands of soldiers). Thus a mile is mille passūs (literally, "a thousand paces"), but two miles is duo milia passuum (literally, "two thousands of paces").
To denote one's age, which in English is expressed in the construction I am ... years old, in Latin one would most commonly say Habeo ... annos (literally, "I have ... years"). The numeral is in the accusative plural, if it declines.