Class 9th Number Systems Practice Tests

Part A: Multiple Choice Questions (MCQs)

1. Which of the following is a rational number?
   a) √3
   b) 0.75
   c) π
   d) √2
2. The decimal expansion of 5/8 is:
   a) 0.625
   b) 0.666…
   c) 0.5
   d) 0.75
3. The sum of two irrational numbers is:
   a) Always rational
   b) Always irrational
   c) Sometimes rational, sometimes irrational
   d) None of these
4. Which number is irrational?
   a) 22/7
   b) √16
   c) √7
   d) 0.25
5. If x = 0.999…, then x equals:
   a) 1
   b) 0.99
   c) 0.9
   d) 0.999

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Part B: Short Answer Questions

6. Express 0.363636… as a rational number in simplest form.
7. Find the rational number between 3/5 and 4/5.
8. Write whether the product of two irrational numbers is always irrational. Justify your answer with an example.
9. Show that √2 is irrational.
10. Write the conjugate of the number (√7 + 2).

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Part C: Long Answer Questions

11. Prove that √3 is an irrational number by contradiction.
12. Find the decimal expansion of 7/12. Is it terminating or non-terminating?
13. Convert 0.2̅3 (0.232323…) into a rational number.
14. Explain the difference between rational and irrational numbers with examples.
15. Calculate the value of (√5 + √3)(√5 − √3) and simplify it.

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Answers (for self-check)

Part A:

1. b
2. a
3. c
4. c
5. a

Part B:
6) 0.363636… = 36/99 = 4/11
7) One rational number between 3/5 and 4/5 is 7/10
8) Product can be rational or irrational. Example: (√2)(√2) = 2 (rational)
9) √2 is irrational — (Proof by contradiction)
10) Conjugate is (√7 − 2)

Part C:
11) Proof by contradiction for √3 is similar to √2’s proof.
12) 7/12 = 0.5833… (non-terminating repeating)
13) 0.2̅3 = 23/99
14) Rational numbers can be expressed as p/q where q ≠ 0; decimal is terminating/repeating. Irrational cannot be expressed as such and decimal is non-terminating, non-repeating.
15) (√5 + √3)(√5 − √3) = 5 − 3 = 2

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