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Number System & Exponents
Rational vs Irrational Numbers
The real number system includes both rational and irrational numbers. Rational Numbers: • Can be written as a fraction a/b (where b ≠ 0) • Decimal form either terminates or repeats • Examples: 1/2, -3, 0.75, 0.333... Irrational Numbers: • Cannot be written as a simple fraction • Decimal form never terminates or repeats • Examples: π, √2, √3, e Every real number is either rational or irrational!
Example:
Determine if these are rational or irrational: √9 = 3 → Rational (can write as 3/1) √10 → Irrational (no perfect square) 0.121212... → Rational (repeating pattern) π = 3.14159... → Irrational (never repeats)