| A. Ordinal Numbers |
Both types of numeral are declined. Ordinal numbers are adjectival in form, and thus simply follow the adjectival declension. In compound ordinals, however, only the final component is in the ordinal (adjectival) form:
| двадцать пятый, twenty-fifth: | |
| двадцать пятого (gen. sing.) двадцать пятом (lос. sing.) двадцать пятых (gen. pl.), etc. | |
The only ordinal number which requires additional explanation is the adjective "third," or третий (m.), третья (f.), третье (n.). Notice that the feminine and neuter adjectival endings are not the expected compound endings -ая (-яя), -ое (-ее). This is so in the nominative and accusative, both singular and plural. The complete declension of this ordinal appears in the Appendix.
| B. Cardinal Numbers |
Declensions of the cardinal numbers are found in the Appendix. Note that only the numbers "one" and "two" distinguish gender; the number "one" has the following forms which follow the declension of этот: один (m.), одна (f.), одно (n.), and одни (pl.); the number "two" exhibits the form два for masculine and neuter nouns and the form две for feminine nouns.
1. Use of case with numbers. Numbers may occur in any of the cases, depending upon their function in the sentence.
a. The number "one" is essentially an adjective, and as such agrees in gender, number, and case with its noun. The plural form, одни, is used when the following noun occurs only in the pluraclass="underline"
Если одни часы колеблются с периодом T, ... → If one clock vibrates with period T, ...
When the number "one" is part of a compound number, both the number "one" and the noun remain in the singular:1
Он написал пятьдесят одну статью. → He wrote fifty-one articles.
The word один may also express the meanings "certain," "alone," and "a":
Одни математики согласились с Лобачевским. → Certain mathematicians agree with Lobachevsky.
одна теорема Лобачевского → a theorem of Lobachevsky
b. When the numbers два, две, три, and четыре (and compounds ending in them) are used in the nominative and inanimate accusative (which looks like the nominative), the accompanying noun appears in the genitive singular:
два примера: (gen. sing. of пример) → two examples
разбить на 2 интеграла (gen. sing. of интеграл) → to split into two integrals
Пусть i, j, k — три вектора единичной длины, ... → Let i, j, k be three vectors of unit length, ...