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Lesson
Number Systems — Complete Lesson
The World of Numbers
All numbers belong to a number system. Let's understand the hierarchy:
Natural Numbers (N): 1, 2, 3, 4, ... (counting numbers)
Whole Numbers (W): 0, 1, 2, 3, ... (natural numbers + zero)
Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ...
Rational Numbers (Q): Numbers expressible as p/q where q ? 0 (e.g., ½, -3/4, 0.75)
Irrational Numbers: Cannot be expressed as p/q (e.g., v2, p, v3)
Real Numbers (R): All rational + irrational numbers
Irrational Numbers
These are non-terminating, non-repeating decimals:
- v2 = 1.41421356... (never ends, never repeats)
- p = 3.14159265... (never ends, never repeats)
Decimal Expansions
| Type | Example | Rational/Irrational? |
|---|---|---|
| Terminating | 0.25, 1.5 | Rational |
| Non-terminating repeating | 0.333..., 1.272727... | Rational |
| Non-terminating non-repeating | v2, p | Irrational |
Laws of Exponents for Real Numbers
a? × an = a??n
(a?)n = a?n
a? / an = a??n
a? × b? = (ab)?
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MCQ Practice
Number Systems — MCQ Practice
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