What is an ordinal number in math?
An ordinal number tells the position of something in an ordered list: first, second, third, fourth and so on. It answers “Which place?” rather than “How many?”. Ordinals are written as words or as a numeral with an ending: 1st, 2nd, 3rd, 4th, 11th, 21st, 22nd.
Ordinal Number in a picture
Formal definition and notation
In everyday mathematics, an ordinal number designates the place occupied by an item in an ordered sequence: the item in position n is the nth item. Ordinals differ from cardinal numbers, which tell how many items a set has. (In set theory, “ordinal” has a further technical meaning, the order type of a well-ordered set, which extends the idea to infinite lists.)
| Symbol | Read it as | Meaning |
|---|---|---|
| 1st, 2nd, 3rd | first, second, third | numeral plus the last letters of the word |
| 4th to 20th | fourth to twentieth | all end in th, including 11th, 12th and 13th |
| nth | n-th | the item in position n, used in rules such as “the nth term of a sequence” |
Key facts
- Cardinal numbers count (3 apples); ordinal numbers order (the 3rd apple).
- Ordinals are used for dates (July 4th), floors (the 2nd floor), places in a race and terms of a sequence.
- If you are the nth person in a line, there are n − 1 people ahead of you.
- In a line of T people, the nth from the front is the (T − n + 1)th from the back.
- Words: first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth; note the spellings fifth, eighth, ninth and twelfth.
Choosing the ending
- exception
- numbers ending in 11, 12 or 13 always take th: 11th, 112th, 213th
- examples
- 31st, 42nd, 53rd, 64th, 100th
Look at the last two digits first. If they are 11, 12 or 13, write th; otherwise look at the last digit.
Ordinal Number examples, step by step
Example 1: Your place in line
There are 4 people ahead of you in line. What is your position?
- The people ahead fill positions 1st to 4th.
- You come next.
Answer: You are 5th in line.
Example 2: Writing ordinal abbreviations
Write 22, 13 and 101 as ordinal numbers with endings.
- 22 ends in 2 (and not 12): 22nd.
- 13 ends in 13: always th, so 13th.
- 101 ends in 01, last digit 1: 101st.
Answer: 22nd, 13th and 101st.
Example 3: Counting from the other end
In a line of 30 students, Maya is 12th from the front. What is her position counting from the back?
- There are 12 − 1 = 11 students in front of Maya.
- Students behind her: 30 − 12 = 18.
- From the back, the 18 students come first, then Maya: position 18 + 1 = 19.
Answer: Maya is 19th from the back.
Common mistakes
Eleventh, twelfth and thirteenth end in “th” when spoken, so their abbreviations end in th too.
Subtracting counts the people behind her; she herself is one more place.
Ordinal words name a single item’s place, not how many items there are.
Not to be confused with
A cardinal number tells how many: there are 7 days in a week. An ordinal tells which one: Saturday is the 7th day (in a week starting Sunday).
A nominal number is only a label, like a jersey number 23 or a phone number. It shows neither amount nor order.
In advanced math, an ordinal is the order type of a well-ordered set, which can be infinite. School math uses the everyday sense: first, second, third.
Quick check: 3 questions
Which ordinal is written correctly?
Answer: C. Numbers ending in 12 always take th, so 12th is correct. 12nd ignores that exception, 21 should be 21st, and 3 should be 3rd.Show answer and explanation
Which sentence uses an ordinal number?
Answer: B. “Third” names a position, so it is ordinal. “9 planets” and “3 pencils” are counts (cardinal), and bus 42 is just a label.Show answer and explanation
Ten runners finish a race. Sam finishes 4th. How many runners finished after Sam?
Answer: D. Positions 5th to 10th come after Sam: 10 − 4 = 6 runners. 3 is the number ahead of him, 4 is his position, and 5 subtracts 5 by mistake.Show answer and explanation
Ordinal Number: frequently asked questions
What is the difference between cardinal and ordinal numbers?
Cardinal numbers count and ordinal numbers order. “There are 6 eggs” uses the cardinal number 6 to say how many. “Take the 6th egg” uses the ordinal number 6th to say which one. Cardinals are one, two, three; ordinals are first, second, third.
Why is it 11th and not 11st?
The abbreviation copies the last letters of the spoken word. We say “eleventh”, “twelfth” and “thirteenth”, so they are written 11th, 12th and 13th. Numbers like 21, 22 and 23 are said “twenty-first”, “twenty-second” and “twenty-third”, so they take st, nd and rd. The same rule covers 111th, 112th and 113th.
Where are ordinal numbers used in math?
Anywhere order matters. Sequences name terms by position: the 5th term of 2, 4, 6, … is 10. Place value talks about the first, second and third digit after the decimal point. Dates, rankings and the steps of a procedure also use ordinals, such as “the 1st step is to order the data“.
Practice and tools
Sources
Updated November 2026·Reviewed by the Effortless Math team·Standards: n/a
Cite this entry
Effortless Math Team. “Ordinal Number.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/ordinal-number/
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