Mei Ling thinks of a 4-digit number. When rounded to the nearest thousand, it becomes 6 000. When rounded to the nearest hundred, it becomes 5 900. When rounded to the nearest ten, it becomes 5 890. What is the smallest possible number she could be thinking of?
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Worked Solution
Step 1: Find numbers that round to 6 000 (nearest thousand).
Range: 5 500 to 6 499.
Step 2: Find numbers that round to 5 900 (nearest hundred).
Range: 5 850 to 5 949.
Step 3: Find numbers that round to 5 890 (nearest ten).
Range: 5 885 to 5 894.
Step 4: Find the intersection of all three ranges.
All three: 5 885 to 5 894.
Step 5: The smallest number in this intersection is 5 885.
Verify 5 885:
Nearest ten: units digit 5 ≥ 5, round up → 5 890 ✓
Nearest hundred: tens digit 8 ≥ 5, round up → 5 900 ✓
Nearest thousand: hundreds digit 9 ≥ 5, round up → 6 000 ✓
Answer: 5 885
Correct answer: 5 885
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