Yes, 0 is a rational number. A rational number is any number that can be expressed in the form p/q where p and q are integers and q ≠ 0. Since 0 = 0/1 (where p = 0, q = 1, and q ≠ 0), zero satisfies the definition of a rational number.
0 is a rational number because 0 = 0/1 (p/q form, q ≠ 0).
0 is also a whole number and an integer.
0 is NOT a natural number (natural numbers start from 1).
0 is neither positive nor negative.
0 is an even number (0 ÷ 2 = 0, remainder 0).
Number set relationship: N ⊂ W ⊂ Z ⊂ Q ⊂ R.
Definition of Rational Number: • A number is rational if it can be written as p/q • where p and q are integers and q ≠ 0
Proof that 0 is Rational: • 0 = 0/1 (p = 0, q = 1, q ≠ 0) ✓ • 0 = 0/2 = 0/3 = 0/(-5) — can be written in infinitely many p/q forms • All forms satisfy the definition → 0 is rational
Is 0 Also Other Types of Number? • 0 is a Whole Number (0, 1, 2, 3...) • 0 is an Integer (...-2, -1, 0, 1, 2...) • 0 is a Rational Number • 0 is NOT a Natural Number (Natural numbers start from 1) • 0 is NOT a Positive or Negative number • 0 is NOT irrational
Number Classification: • Natural Numbers (N): 1, 2, 3, 4... • Whole Numbers (W): 0, 1, 2, 3... • Integers (Z): ...-2, -1, 0, 1, 2... • Rational Numbers (Q): p/q form (includes all integers, fractions, decimals) • Irrational Numbers: √2, π, e (cannot be written as p/q) • Real Numbers (R): Rational + Irrational
Relationship: N ⊂ W ⊂ Z ⊂ Q ⊂ R
Important Properties of 0: • Additive identity: n + 0 = n • Multiplicative zero: n × 0 = 0 • 0 ÷ n = 0 (for n ≠ 0); but n ÷ 0 = undefined • 0 is neither positive nor negative • 0 is even (divisible by 2: 0/2 = 0)
Common Exam Question: 'Is 0 a rational number? Justify.' → Answer: Yes. 0 = 0/1, which is in p/q form where q ≠ 0. Hence 0 is rational.
Yes, 0 is a rational number. A rational number is defined as any number expressible in the form p/q where p, q are integers and q ≠ 0. Since 0 can be written as 0/1 (where p = 0, q = 1, and q ≠ 0), it satisfies this definition. 0 is also a whole number and integer, but NOT a natural number (which starts from 1).
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