Cardinal vs Ordinal Numbers: Writing Them Correctly in Words

Cardinal and ordinal numbers are frequently used in writing, often without realizing the distinction. Release notes may mention "second major release," error messages might state "the first argument must be a string," and UI copy could announce "you came in third place." Despite these common uses, the difference between cardinal and ordinal numbers can confuse even seasoned writers. Let's clarify.

Cardinal numbers answer the question "how many?" They indicate quantity. Examples include one, two, three, twelve, forty-seven, and two hundred and thirteen. In programming, arrays have lengths, queues have sizes, and APIs return counts—all cardinal numbers. For instance, "the function accepts three arguments" or "there are 12 pending jobs in the queue."

Ordinal numbers, on the other hand, address "in what position?" They describe rank or sequence. Examples are first, second, third, twelfth, forty-seventh, and two hundred and thirteenth. Think of leaderboard positions, sorting results, pagination, race finishing orders, and version histories. For example, "this is the first public beta" or "she finished twenty-third out of five hundred runners."

The general rule for forming ordinals is adding -th to the cardinal number, such as four → fourth, nine → ninth, twenty → twentieth. However, there are irregulars to remember: one → first, two → second, three → third, five → fifth, eight → eighth, nine → ninth (dropping the e), and twelve → twelfth (where ve becomes f). Compound numbers also follow this pattern, with only the last part becoming ordinal: thirty-one → thirty-first, one hundred and two → one hundred and second.

When writing fractions or abbreviated forms in documentation, many mistakes occur. In technical writing, you might see abbreviated ordinals like 1st, 2nd, 3rd, and 4th. The general pattern is using the last two letters of the full word (fir* st, seco nd, thi rd, four th) with exceptions for 11th, 12th, and 13th, which all take th (eleventh, twelfth, thirteenth). That's why "the 21st century" works but "21th" is incorrect, while "the 13th of October" is correct, and "13rd" is wrong.

To decide whether to use cardinal or ordinal numbers, ask which question the number answers. If the question is "how many?"—cardinal. If it's "in what position?"—ordinal. For example, "The endpoint returned five results" (cardinal) versus "use the fifth result" (ordinal). Similarly, "upgrade to the third release" (ordinal) versus "retry after ten seconds" (cardinal).

A common UI copy mistake is writing "You are number 3 in line." While acceptable in casual products, "You are third in line" reads more naturally and professionally. Another example is writing "the 1st argument" in documentation. While digits with suffixes (step 3 of 7) work well in tables or compact UI labels, spelled-out ordinals (the first argument) often look better in prose.

Consistency is key. Whether in codebases, documentation sites, or product copy, applying the same conventions everywhere—dates, versions, error messages, and changelog entries—helps maintain trust. Use free online tools to confirm spellings if needed. By mastering cardinals and ordinals, your writing—whether in code, documentation, or product copy—will reflect the precision of the software it describes.