Cardinal Numbers
Elementary School
Definition
Numbers that are used for counting. Examples of this includes one, two, three and four. It deals with "how many" there are of something. Cardinal numbers do not have decimals or fractions. They are simple numbers that allows us to carry out counting. Its counterpart is ordinal numbers, which are used to identify the position of something.
Worked examples
\(1, 2, 3, 4, 5, \ldots\)
These are cardinal numbers — they tell you how many objects you have, not their position.
There are \(12\) students in the room.
The number \(12\) is a cardinal number because it answers 'how many students?'
Common mistakes
- \(3.5\) is a cardinal number → Cardinal numbers are whole numbers only: \(1, 2, 3, \ldots\) Cardinal numbers cannot have decimals or fractions — they are used for counting discrete objects.
- Zero \((0)\) is not a cardinal number → \(0\) is a cardinal number Zero tells you 'how many' when there are none of something, so it counts as a cardinal number.
- Using 'third' \((3\)rd\()\) when counting three items → Use \(3\) for counting; 'third' is ordinal (position) Cardinal numbers answer 'how many?'; ordinal numbers like 'third' answer 'which position?'
Where you'll use it next
Cardinal numbers are the foundation for all arithmetic operations, set theory (cardinality), and data analysis where you count occurrences or measure quantities without fractions.
Found in 1 StudyPug lesson
Cardinal Numbers: The Foundation of Counting and Mathematics
5th Grade5thGrade 5 Math placeholder
Dive into the world of cardinal numbers! Learn how these fundamental counting numbers form the basis of mathematics and everyday calculations. Master counting, quantity, and basic arithmetic with our comprehensive guide.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026