Number System ke basics: number types (Natural/Whole/Integer/Rational/Irrational/Real), classification rules, examples, shortcuts aur SSC CGL level practice questions.
Number System me numbers ko unke nature ke basis par classify kiya jata hai:
counting, zero, negative, fractions, decimals, roots, etc.
SSC CGL me yahi classification aage ke topics (HCF/LCM, remainder, unit digit, factorial) ka base hota hai.
Classification (quick map)
Set
Symbol
Contains
Examples
Natural Numbers
N
Counting numbers (1 se start)
1, 2, 3, 10, 99
Whole Numbers
W
Natural + 0
0, 1, 2, 50
Integers
Z
Negative + 0 + Positive
..., -3, -2, -1, 0, 1, 2, 3, ...
Rational Numbers
Q
p/q form (q ≠ 0), terminating/recurring decimals
3/5, -7/2, 0.125, 2.333...
Irrational Numbers
Q′
Non-terminating, non-recurring decimals
√2, √3, π
Real Numbers
R
Rational + Irrational (sab number line par)
-5, 2/3, √2, 3.14
Fast rules (SSC CGL favorites)
Terminating decimal ⇒ Rational
Recurring decimal ⇒ Rational
Non-terminating + Non-recurring ⇒ Irrational
√(perfect square) ⇒ Integer / Rational
√(non-perfect square) ⇒ Irrational
Examples
0 whole number hai, integer hai, rational hai (0 = 0/1), real hai. Natural (SSC pattern) me usually include nahi hota.
-7 integer, rational (-7 = -7/1), real.
0.375 terminating ⇒ rational (375/1000 = 3/8).
1.272727... recurring ⇒ rational.
√49 = 7 integer/rational.
√2 irrational.
Common traps
Natural numbers me 0 ko include karna—SSC me mostly N = {1,2,3,...} follow hota hai.
Decimal dikhe to irrational maan lena—recurring decimal rational hota hai.
Root dikhe to irrational maan lena—perfect square ka root integer hota hai.
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