Number System
Gujarat Board · Class 9 · Mathematics
Quick revision notes for Number System — Gujarat Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Types of Numbers and Their Relationships
- Natural numbers (N): 1, 2, 3, 4, ... - counting numbers used in daily life
- Whole numbers (W): 0, 1, 2, 3, ... - natural numbers including zero
- Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ... - whole numbers including negatives
Irrational Numbers and Number Line Representation
- Examples of irrational numbers: √2, √3, √5, π, 0.101100111000111...
- √2 was the first irrational number discovered by Pythagoreans around 400 BC
- Irrational numbers have non-terminating, non-recurring decimal expansions
Decimal Expansions of Real Numbers
- Rational numbers have either terminating or non-terminating recurring decimal expansions
- Terminating decimals: remainder becomes zero (e.g., 7/8 = 0.875)
- Non-terminating recurring: remainder repeats (e.g., 1/3 = 0.3̄, 1/7 = 0.142857̄)
Operations on Real Numbers
- Sum/difference of rational and irrational is always irrational
- Product/quotient of non-zero rational and irrational is always irrational
- Sum/difference/product/quotient of two irrationals may be rational or irrational
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