How to Use Cardinal and Ordinal Numbers
  • 4-minute read
  • 24th October 2018

How to Use Cardinal and Ordinal Numbers

Did you know there are different types of numbers? Two common types are “cardinal numbers” and “ordinal numbers.” And even if you don’t know what these terms mean, you probably use both in your writing regularly. Let’s take a look at how to use cardinal and ordinal numbers.

Cardinal Numbers (Numbers for Counting)

Cardinal numbers are the numbers we count with and probably what you think of first when you hear the word “number.” For example, “one,” “two,” and “three” are all cardinal numbers.

Numbers not affiliated with their bird namesakes.
Numbers not affiliated with their bird namesakes.

You can write these numbers as either words (e.g., eight) or numerals (e.g., 8). Typically, in formal writing, you should write numbers up to ten as words and use numerals for larger values. However, different style guides have different rules on this, so make sure to check yours if you have one.

Ordinal Numbers (Numbers for Ranking)

Ordinal numbers are used to rank or order things (e.g., first, second, third). This could include placement in a race or competition, or it could simply be the day of the month (e.g., December 1st).

Let’s take a look at the first few ordinal numbers to see how they work:

  • First (1st)
  • Second (2nd)
  • Third (3rd)
  • Fourth (4th)
  • Fifth (5th)
  • Sixth (6th)
  • Seventh (7th)
  • Eighth (8th)
  • Ninth (9th)
  • Tenth (10th)
You can use these as the basis for creating other ordinal numbers.

How to Write Ordinal Numbers

You’ll notice above that writing an ordinal number as a numeral involves adding the last two letters from the word (e.g. fourth = 4th). To know which letters to add, follow this guideline:

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  • If the numeral ends in 1, add “st” (e.g., twenty-first = 21st)
  • If the numeral ends in 2, add “nd” (e.g., thirty-second = 32nd)
  • If the numeral ends in 3, add “rd” (e.g., forty-third = 43rd)
  • If the numeral ends in 4, 5, 6, 7, 8, 9, or 0, add “th” (e.g., fifty-sixth = 56th)

The only exceptions to this are “eleventh” (11th), “twelfth” (12th), and “thirteenth” (13th). In addition, any numeral that ends 11, 12, or 13 will end “th” when written as an ordinal number (e.g., 113th). We also have a few tips to share about how to write ordinal numbers in different situations:

  • Most ordinal numbers are written as words when part of a sentence, especially in formal writing, but larger values can be written as numerals.
  • Letters at the end of an ordinal numeral are often written in superscript, as shown above, but this is optional (e.g., you could write either “1st” or “1st”).
  • Written as words, you can add “-ly” to ordinal numbers (e.g., “firstly” or “secondly”). This is common when setting out steps in a process, but you should avoid “-ly” endings with ordinal numbers over nine.

Nominal Numbers (Numbers That Aren’t Numbers)

Finally, you may also hear people mention “nominal” numbers. These include things like phone numbers, barcodes, and the numbers of the back of football players’ shirts: i.e., numbers that name or identify something. Nominal numbers are almost always written as numerals.

Some nominal numbers.
Some nominal numbers.
(U.S. Air Force photo/Master Sgt. Matt Summers)

Summary: Cardinal and Ordinal Numbers

We can sum up cardinal and ordinal numbers as follows:

  • We use cardinal numbers to count (e.g., one, two, three). Typically, in formal writing, you will want to write out numbers up to ten as words and use numerals for larger values.
  • We use ordinal numbers to rank or order things (e.g., first, second, third). Most ordinal numbers are written as words in formal writing, but larger values can be written as numerals.

If you need help checking that you’ve used numbers correctly in your written work, moreover, get in touch with Proofed today.

Comments (7)
Kenneth Sullivan
16th March 2021 at 16:22
I am learning to write numbers as ordinals. I understand the rules of writing cardinals as words when they are one through 9; when they are 10 and over, write them in number form. Does this rule also apply to ordinals? Writing ordinals in words when the numbers are one through 9; write ordinals in number form when the numbers are 10 and over?
    Proofed
    17th March 2021 at 08:33
    Hi, Kenneth. As a rule of thumb, you would write out most ordinal numbers as words in formal writing, even larger ones (e.g., in an essay, you would write "The thirteenth example we would like to highlight," rather than "The 13th example we would like to highlight"). However, you might use numerals if writing out an ordinal in words would be awkward (e.g., "The one thousand four hundred and eighty-sixth winner of the prize..." would be better as "The 1,486th winner of the prize..."), and there is plenty of leeway in less formal writing, where it is largely a matter of preference. Some style guides will have specific rules for writing ordinals, too.
Amy Asch
20th May 2021 at 11:20
Is it correct to use the ordinal form in a date with a year, such as "April 21st, 2020"? Or should it always be the cardinal form when followed by a year: "April 21, 2020"? Thank you! P.S. I see the comment and answer above mine are dated in the form: 16th March 2021. I would have to use the American date format. Thanks!
    Proofed
    20th May 2021 at 11:28
    Hi, Amy. Most style guides suggest dropping the ordinal suffix in the US date format (including AP style and Chicago). Ultimately, though, if you're not using a specific style guide, you can use whichever form you prefer.
Amy Fara Asch
27th May 2021 at 20:52
Thank you so much
Raju
21st July 2021 at 18:51
Hello sir,madam! is it correct to write this certificate is awarded to ms.Gita for securing 1st position or first position?which is right to use?And can we use articl the before that ordinal number or not
    Proofed
    22nd July 2021 at 09:01
    Hi, Raju. Either "1st position" or "first position" is acceptable in general usage, but you may want to check your style guide for advice on writing numbers if you have one (e.g., many style guides suggest writing out numbers under 10 as words, so in that case "first position" would be correct). And you can use an article before an ordinal as long as it makes sense in context (e.g., "A first place finish will enhance your reputation"), but I don't think you'd need an article in your example.

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