Irrational Numbers Flashcards

Grade 8 · Math · Flashcards

Key definitions and examples for classifying and estimating irrational numbers.

Flashcards

Rational number: Can be written as p/q (integer over nonzero integer); decimal terminates or repeats
Irrational number: Cannot be written as p/q; decimal is infinite and non-repeating
Real numbers: All rational and irrational numbers; every point on the number line
Perfect square: An integer whose square root is also an integer: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
√2: ≈ 1.414; irrational; the diagonal of a 1×1 square
π (pi): ≈ 3.14159; irrational; ratio of a circle's circumference to its diameter
Terminating decimal: A decimal that ends (e.g., 0.25); always rational
Repeating decimal: A decimal with an infinitely repeating block (e.g., 0.333…); always rational
Non-repeating decimal: Never forms a repeating block; characteristic of irrational numbers
Estimating √n: Find perfect squares A² and B² so A² < n < B²; √n is between A and B
Classifying √n: If n is a perfect square, √n is rational; otherwise √n is irrational
Number line placement: Irrational numbers have exact positions on the number line despite being non-repeating decimals