I'll work through each problem step by step to find the correct answers.
Problem 1: Order 3π, √10, and 3.25 from least to greatest.
Let me calculate approximate values:
- π ≈ 3.14159...
- 3π ≈ 3 × 3.14159 ≈ 9.42
- √10 ≈ 3.16 (since 3² = 9 and 3.2² = 10.24)
- 3.25 is already given
Ordering from least to greatest: 3.16 < 3.25 < 9.42
So: √10 < 3.25 < 3π
Answer: B
Problem 2: Between which two whole numbers is the square root of 277?
Let me check perfect squares near 277:
- 16² = 256
- 17² = 289
Since 256 < 277 < 289, we have √256 < √277 < √289
Therefore: 16 < √277 < 17
Answer: B
Problem 3: Between which two whole numbers is √5?
Let me check perfect squares near 5:
- 2² = 4
- 3² = 9
Since 4 < 5 < 9, we have √4 < √5 < √9
Therefore: 2 < √5 < 3
Answer: B
Problem 4: Order from least to greatest: [10, -5, 3, 16, -1, 0, 1]
Arranging in order from smallest to largest:
-5, -1, 0, 1, 3, 10, 16
Answer: B
Problem 5: List from least to greatest: -64, 3.5, √27, 6.666...
Let me calculate √27:
√27 ≈ 5.20 (since 5² = 25 and 5.2² = 27.04)
Now ordering: -64 < 3.5 < 5.20 < 6.666...
So: -64, 3.5, √27, 6.666...
Answer: D
Problem 6: Point B could represent which number?
Looking at the number line, point B appears to be between 5 and 5.5, closer to 5.
Let me check the options:
- √30 ≈ 5.48 (since 5.48² ≈ 30)
- √24 ≈ 4.90 (since 4.9² ≈ 24)
Point B is between 5 and 5.5, so it's approximately 5.2-5.5.
√30 ≈ 5.48 fits this range better than √24 ≈ 4.90.
Answer: A
Final Answer:
1. B
2. B
3. B
4. B
5. D
6. A
Parent Tip: Review the logic above to help your child master the concept of ordering real numbers practice worksheet.
