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Sameer writes and says it is a rational number because 9 and 0 are both integers. Is he right?

Class 7Rational NumbersRational Numbers
  • ANo — a rational number must have a NON-ZERO denominator, and is not defined
  • BYes — 9 and 0 are both integers, so fits the form p/q
  • CYes — is just another way of writing 0
  • DNo — 9 and 0 share no common factor, so it cannot be simplified

Step-by-Step Solution

The definition is p/q with p, q integers AND q not equal to 0. Sameer stops at "both are integers" and forgets the second half of the rule, so is not defined and is not rational. Note the reverse case IS fine: is a perfectly good rational number — zero is only banned in the denominator.
Answer: A) No — a rational number must have a NON-ZERO denominator, and is not defined

Key idea: Recognising rationals

If you can write a number as **integer over non-zero integer**, it is rational. So:

- All integers are rational: 5 = 5/1, 0 = 0/1, −9 = −9/1.
- All fractions with integer numerator and denominator are rational: 3/4, −2/7, 11/3.
- Any decimal that terminates or repeats is rational: 0.25 = 1/4, 0.333… = 1/3.

Numbers that cannot be written as p/q (like √2 or π) are NOT rational — they're irrational. You'll meet those in Class 9.

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