Cardinal Ordinal and Nominal Numbers

There are some who believe that a number is just a number—no big deal. However, numbers are quite fascinating and diverse. Indeed, one can classify numbers in several ways. Cardinal, ordinal and nominal numbers are common number types that we come across in our daily lives—even though we might not know which is which.

A cardinal number represents quantity, amount or value. When you state your age, read a price or count sheep, you are using cardinal numbers.  Such numbers are also known as “counting numbers” and represent a quantity in reality. Both numbers and words can represent cardinal numbers. One, one thousand and fifty are the lexical representation of cardinal numbers. 1, 100 and 12 are the numeric form of cardinal numbers. Since cardinal numbers represent quantity, if you state your age, for e.g. 30, you have already lived for 30 completed years.

An ordinal number refers to the order or place of a number in a set. Therefore, ordinal numbers are relational. When you identify the place of an athlete in a race, for example, you are using an ordinal number. Ordinal numbers exclusively indicate pace, rank or position. Just like cardinal numbers, words and numbers can represent ordinal numbers. First, Fifty-ninth and tenth are lexical representations of ordinal numbers. In numeric form, these would be 1st, 59th and 10th. If your age is 30, as in the example for cardinal numbers, you would be quite correct in stating that you are in your 31st year.

Nominal numbers are somewhat arbitrary. They usually represent something meaningful but are not defined within a set and do not represent quantity. Since we use numbers to identify persons, concepts and objects, nominal numbers are very useful and common in everyday life. Your Social Security number is a common nominal number. Another example is the number on an athlete’s uniform. Any number that represents something besides quantity or position/rank is a nominal number.

You can state the date in either ordinal or cardinal form. For instance, if you state the date as December 31 2009, you are stating it as a cardinal number. However, if you state the date as December 31st 2009, you are using the ordinal form. The way we represent the year in a date led to some contention over when the new millennium began circa 2000.

Several persons argued that the millennium began at the start of 2001 instead of in 2000. The key to the answer is the difference between ordinal and cardinal numbers. Although, we represent the year as a cardinal number, it is really an ordinal number. The calendar started at 1 A.D., representing the 1st Year of Our Lord. Therefore, since the year is ordinal, the millennium began at the start of 2001.