Rational and Irrational Numbers
Numbers can be classified as rational (expressible as a fraction) or irrational (non-terminating, non-repeating decimals). Understanding this classification deepens number sense.
What You Need to Know
Key Concept Diagram
A rational number can be written as p/q where p and q are integers and q is not zero
Irrational numbers cannot be expressed as fractions; their decimals never repeat or terminate
Square roots of non-perfect squares are irrational (e.g. root 2, root 3)
Pi and e are famous irrational numbers that appear throughout mathematics
Key Vocabulary
Rational number
A number that can be written as a fraction of two integers
Irrational number
A number whose decimal expansion is non-terminating and non-repeating
Perfect square
An integer that is the square of another integer (1, 4, 9, 16, 25...)
Real number
All rational and irrational numbers together make up the real numbers
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Which of the following is irrational?
Question 2
Is 0.333... (repeating) rational or irrational?
Question 3
Between which two consecutive integers does root(30) lie?
Key Concepts Summary
- ●A rational number can be written as p/q where p and q are integers and q is not zero
- ●Irrational numbers cannot be expressed as fractions; their decimals never repeat or terminate
- ●Square roots of non-perfect squares are irrational (e.g. root 2, root 3)
- ●Pi and e are famous irrational numbers that appear throughout mathematics