Ordinal numbers: What they are

Ordinal numbers are an essential part of everyday language and mathematics, helping us describe the position or order of items in a sequence. Whether you’re talking about finishing first in a race or picking the third book on a shelf, ordinal numbers answer the question “which one?” Originally defined by mathematician Georg Cantor, these numbers differ from their cardinal counterparts by focusing on rank rather than quantity. This guide explores what ordinal numbers are, how they work, and how to use them effectively in both words and numerals.

Ordinal numbers tell us the position or order of something in a sequence. They answer the question “which one?” and are commonly used in speaking. Just as with cardinal numbers, these numbers were defined by the mathematician Georg Cantor.

Think of them like this: if you’re in a race, you might come in first, second, or third place. Those “first,” “second,” and “third” are ordinal numbers.

Here are some key things about ordinal numbers:

• Position: They indicate the place of something in a list or order.  
• Sequence: They show the order of items in a series.  
• Examples: first, second, third, fourth, fifth, tenth, hundredth, and so on.

Difference between cardinal and ordinal numbers

It’s important to remember the difference between cardinal and ordinal numbers:

• Cardinal numbers: Tell us “how many” (e.g., 3 apples)  
• Ordinal numbers: Tell us the position or order (e.g., the 3rd apple in the line)  

How to write ordinal numbers

• In words: first, second, third, fourth, fifth, sixth, seventh, eighth, ninth
• In numerals: 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th
• For numbers 10 and above: you usually add “th” to the end of the cardinal number (e.g., 10th, 11th, 20th, 100th). There are some exceptions, like 21st, 22nd, and 23rd.

In summary

Ordinal numbers indicate the position or sequence of something in a list, such as “first,” “second,” or “third,” unlike cardinal numbers, which count “how many” (e.g., 1, 2, 3). Defined by Georg Cantor, ordinal numbers are widely used in speech and writing to organize and rank items. They are written as words (e.g., “fourth”) or numerals with suffixes like “st,” “nd,” “rd,” or “th” (e.g., 1st, 2nd, 3rd, 4th), with rules varying slightly for numbers like 21st or 23rd. From “first” to “thousandth,” ordinal numbers provide a clear way to express order in any context.