Ordinal numbers

An ordinal number is a number used to tell order, or position. Ordinal numbers are often discussed alongside cardinal numbers and nominal numbers.

A podium is a common example of ordinal numbers that typically shows the first, second, and third place contestants in an event. First place is the position of the winner of the event, followed by second place, then third place.

On a podium, the order is typically indicated using height; first place is positioned the highest, and third place the lowest. It is not uncommon to list numbers from top to bottom, where 1st is the topmost number. Another common way that ordinal numbers may be organized is from left to right, with 1st being the position furthest to the left. There are many other ways a set of ordinal numbers can be organized. For example, in a race, 1st position is determined relative to the finish line; the person closest to the finish line is in 1st. If there were 20 people in the race, the person furthest from the finish line would be in 20th place.

Each ordinal number can be paired with a cardinal number (a whole number that tells how many of an object there are in a group):

Ordinal number   Cardinal number
first   one, or 1
second   two, or 2
third   three, or 3
fourth   four, or 4
tenth   ten, or 10
twenty-first   twenty-one, or 21
hundredth   one hundred, or 100

Ordinal, cardinal, and nominal numbers

These three types of numbers are often discussed together since it is necessary to understand them in order to effectively communicate using numbers. Briefly, a cardinal number differs from an ordinal number in that cardinal numbers are used for counting and identifying how many of something there are, rather than being a reference to position or rank.

Nominal numbers, unlike ordinal numbers, are used mainly for identification purposes. Nominal numbers, like a phone number or a zip code, don't tell us anything about any actual value, rank, position, etc. They are just used to name or distinguish elements within a set of similar objects.

As an example that includes the use of all three types of numbers, imagine that there are 15 people running in a race. 15 is a cardinal number. The participants in the race are assigned the numbers 1-15 depending on when they registered for the race. Their respective numbers are nominal numbers. Only the three people who finish the race fastest get a prize based on whether they ranked first, second, or third. First, second, and third are ordinal numbers.