A. J. Lohwater's Russian-English Dictionary of the Mathematical Sciences

106	миллион; миллионный, -ая, -ое
109	миллиард; миллиардный, -ая, -ое
1012	биллион; биллионный, -ая, -ое

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 plural:

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, ...

If the noun following the number is preceded by an adjective, it may be in either the genitive plural or the nominative plural (although the noun is genitive singular in both instances). Generally, the genitive plural is used with masculine and neuter nouns, while the nominative plural is used with feminine nouns:

три сложных примера > three complex examples (masculine noun)

три сложные книги > three complex books (feminine noun)

Вводя три единичных вектора i₁, i₂, i₃, ... > If we introduce the three unit vectors i₁, i₂, i₃, ...

If the item following the number is a substantivized adjective, that is, an adjective acting as a noun, the word is treated as an adjective under the above conditions:

две переменных > two variables

две кривые > two curves

c. When the numbers пять (five) and up through девятнадцать (nineteen), and any compound numbers ending in five, six, seven, eight, nine, or zero are in the nominative or inanimate accusative cases, both the noun and its adjective appear in the genitive plural: