Noun

1. A word that expresses the relative position of an item in an ordered sequence.

   First, second and third are the ordinal numbers corresponding to one, two and three.

2. A number used to denote position in a sequence.

   In the expression a₃, the "3" is an ordinal number.

3. A generalized kind of number to denote the size of a well-ordered set.

Usage notes

• Ordinal numbers are general construed as adjectives preceding nouns in singular:

  eleventh day

• Ordinal numbers are used for fractions as nouns, and for exponents usually followed by power and that numeral:

  two fifths, $\backslash textstyle\backslash frac\{2\}\{5\}$

  two to the minus twenty-first power, $2^\{-21\}$

  six to the third, $6^3$

• Ordinal numbers are generally considered to be ordered from high to low, so that first place is considered highest, and fifth is lower than second. Degree is an exception.
• Ordinal numbers corresponding to numbers higher than 20 use cardinal numbers for all the places preceding the final ordinal part:

  twenty-first or 21st, occasionally XXI

  one hundred fifteenth or 115th , occasionally CXV

  thirty-three thousandth or 33,000th

• If an ordinal is followed by a plural noun, the two word phrase refers to a set of items described by the phrase in singular. For example second homes refers to a set of homes which are considered a "second home."

  Many households have third cars.