1. Which is irrational?
- A
- B0.625
- C
- D
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Answer: C)
= 4, has non-terminating non-recurring decimal expansion → irrational. 0.625 and are rational.
Class 9 Number Systems — practice questions with answers
Number Systems · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. The number 0.101001000100001… (with an increasing number of zeros) is:
- AIrrational
- BRational (terminating)
- CRational (recurring)
- DAn integer
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Answer: A) Irrational
The pattern of zeros keeps increasing, so the decimal never terminates and never repeats a fixed block. Non-terminating non-recurring → irrational.
3. The value of (16)^(1/2) + (16)^(1/4) is:
- A12
- B5
- C7
- D6
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Answer: D) 6
(16)^(1/2) = = 4 and (16)^(1/4) = = 2. Sum = 4 + 2 = 6.
4. A number line is examined in stages — first between 3 and 4, then between 3.7 and 3.8, then between 3.76 and 3.77 — in order to locate 3.765. This visualising process is called:
- ASuccessive magnification
- BRationalisation
- CPrime factorisation
- DConjugation
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Answer: A) Successive magnification
Each stage “zooms in” on a smaller interval containing the number, so the decimal is pinned down one place at a time. This is called successive magnification. The other three are algebraic techniques, not number-line ones.
5. Which of these is an IRRATIONAL number lying between 2 and 3?
- A
- B
- C
- D
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Answer: D)
Between 2 and 3 means between and , so any with 4 < n < 9 works: ≈ 2.236. ≈ 1.73 is too small, ≈ 3.16 is too big, and is in range but rational.
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