Irrational numbers and Pi
Irrational Numbers and Pi
Irrational Numbers and Pi is a topic in Numbers & Operations in the Texas Essential Knowledge and Skills. It is aligned to Standard 8.2(A), which requires students to distinguish rational from irrational numbers, including pi.
An irrational number cannot be written as a fraction; its decimal never terminates or repeats, as with \(\pi\) and \(\sqrt2\).
Theory
An irrational number cannot be written as a fraction of integers; its decimal never terminates or repeats.
The two groups:
How to classify a number
- Check if it can be a fraction of integers.
- Terminating or repeating decimal: rational.
- Non-terminating, non-repeating: irrational.
- Roots of non-perfect squares are irrational.
Its decimal never terminates or repeats β irrational.
It terminates and equals \(\dfrac14\) β rational.
No β its decimal never repeats, so it is irrational.
No β \(\sqrt9=3\), a whole number, so it is rational.
Common pitfalls
Frequently asked questions
What is an irrational number?
A number that cannot be written as a fraction.
Is pi irrational?
Yes.
Is \(\sqrt2\) irrational?
Yes.
Is \(\sqrt9\) irrational?
No, it equals \(3\).