Cardinal numbers: What they are

Counting numbers (cardinal numbers)

Cardinal numbers are the numbers we use for counting. This theory came from a mathematician named Georg Cantor. They answer the question “how many?”  So, you can think of them as the numbers you learned first: 1, 2, 3, 4, and so on. They represent the quantity of something, whether it’s apples in a basket, students in a class, or stars in the sky. Don’t confuse these with ordinal numbers.

Here are some key things to understand about cardinal numbers:

• Counting: They’re the numbers we use to count things.  
• Quantity: They tell us “how many” of something exists.  
• Whole numbers: They are whole numbers (no fractions or decimals).  
• Examples: 1, 5, 10, 100, 1000, 10000, and so on. Note: We often put a comma after the hundreds place but didn’t here for reading purposes. For example: 1,000 or 10,000.

Remember, cardinal numbers are part of a larger theory that isn’t really pertinent or necessary to English learning unless you want to be a mathematician or have to use advanced mathematics.

List of cardinal numbers

This is a list of numbers from 1 to 20 in both numerical form and word form.

1 – One	6 – Six	11 – Eleven	16 – Sixteen
2 – Two	7 – Seven	12 – Twelve	17 – Seventeen
3 – Three	8 – Eight	13 – Thirteen	18 – Eighteen
4 – Four	9 – Nine	14 – Fourteen	19 – Nineteen
5 – Five	10 – Ten	15 – Fifteen	20 – Twenty

We often think of numbers in blocks or multiples of 10.

10 – Ten	60 – Sixty
20 – Twenty	70 – Seventy
30 – Thirty	80 – Eighty
40 – Forty	90 – Ninety
50 – Fifty	100 – Hundred

So in forming the numbers between these, we would have written numbers such as twenty-one, thirty-two, sixty-five, etc. With the number 100, we would write one hundred, but then follow this form when writing numbers greater than 100: one hundred twenty-five (125) or one hundred ninety-five (195). As you can see, this is a bit cumbersome. In other words, they would be very inefficient and overly complicated to write. So, depending on the writing style or style guide, we usually write out numbers over nine.

Cardinal numbers ranging from 100 to 1000

100	One hundred
200	Two hundred
300	Three hundred
400	Four hundred
500	Five hundred
600	Six hundred
700	Seven hundred
800	Eight hundred
900	Nine hundred
1000	One thousand

Larger counting numbers

10,000	Ten Thousand
100,000	One hundred thousand
1,000,000	One million
10,000,000	Ten million
100,000,000	One hundred million
1,000,000,000	One billion
1,000,000,000,000	One trillion

Abbreviations for cardinal numbers

As you can see, using larger numbers gets a little bit cumbersome whether you are using numbers or word form. We often abbreviate the thousands, billions, and trillions.

Here are some other common abbreviations:

• K – for thousands (e.g., 10K = 10,000)
• B – for billions (e.g., 2B = 2,000,000,000)
• T – for trillions (e.g., 5T = 5,000,000,000,000)

You can also use a combination of these abbreviations. For example, you could write 1.25 billion as 1.25B or 1,250M (The last is rarely used and would be confusing even for some native speakers). When abbreviating numbers, it’s important to be clear about what you mean. If you’re not sure whether your audience will understand your abbreviation, it’s always best to write out the full number. For this reason, it is probably best not to use a number like “1,250M.”

Lastly, remember the number’s place.

In mathematics, the “place” of a number refers to its position in a number and determines its value. This is called place value.  

Our number system is based on powers of 10, and each place represents a different power of 10. Here’s a basic breakdown using the number 2,125:

• Ones place: The rightmost digit represents the number of ones (5 ones).  
• Tens place: The next digit to the left represents the number of tens (2 tens).
• Hundreds place: The next digit represents the number of hundreds (1 hundred).
• Thousands place: The next digit represents the number of thousands (2 thousands), and so on.