∴
Irrational Numbers
Middle School
Definition
A number that cannot be expressed as a fraction, with infinite non-repeating decimal expansion.
Formulas
√2 = 1.41421356...
Square root of 2 (infinite non-repeating decimal)
π = 3.14159265...
Pi
e = 2.71828182...
Euler's number e
Examples
Example 1
Explain why √2 is irrational.
Example 2
Select the irrational numbers: √4, √5, 0.25, π/2
Applications
Geometry
Diagonal lengths, circle circumference
Physics
Growth/decay using Euler's number e
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