- A
- B
- C
- D
Step-by-Step Solution
and . The second list gives 0.625, 0.6875, 0.71875 — all inside. In the first list and fall outside; the third list is entirely below 0.5 and the fourth entirely above 0.75.
Answer: B)
Which list contains three rational numbers that ALL lie between and ?
Class 9Number SystemsNumber Systems
Key idea: Number-system hierarchy
Each system contains the previous one:
ℕ ⊂ W ⊂ ℤ ⊂ ℚ ⊂ ℝ
- Natural → add 0 → Whole.
- Whole → add negatives → Integers.
- Integers → allow division (with q ≠ 0) → Rationals.
- Rationals → fill the gaps with irrationals → Reals.
At every step, the new system contains the old, plus more numbers. Real numbers fill the line completely — there are NO gaps in ℝ.
ℕ ⊂ W ⊂ ℤ ⊂ ℚ ⊂ ℝ
- Natural → add 0 → Whole.
- Whole → add negatives → Integers.
- Integers → allow division (with q ≠ 0) → Rationals.
- Rationals → fill the gaps with irrationals → Reals.
At every step, the new system contains the old, plus more numbers. Real numbers fill the line completely — there are NO gaps in ℝ.
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