Question

match the following expressions to the corresponding points on the number line:$sqrt{0.81}$, $sqrt{8}$, $sqrt{12}$, $sqrt{1.2}$, $\frac{19}{9}$, $\frac{1}{8}$, $-sqrt{10.24}$, $-\frac{10}{7}$, $-\frac{23}{9}$, $-\frac{3}{7}$

Explanation:

Step1: Calculate each value

1. $\sqrt{0.81} = 0.9$
2. $\sqrt{8} \approx 2.83$
3. $\sqrt{12} \approx 3.46$
4. $\sqrt{1.2} \approx 1.10$
5. $\frac{19}{9} \approx 2.11$
6. $\frac{1}{8} = 0.125$
7. $-\sqrt{10.24} = -3.2$
8. $-\frac{10}{7} \approx -1.43$
9. $-\frac{23}{9} \approx -2.56$
10. $-\frac{3}{7} \approx -0.43$

Step2: Match to number line points

• Point A (between 2 and 3, closer to 2): $\frac{19}{9} \approx 2.11$
• Point B (between -1 and 0, closer to 0): $-\frac{3}{7} \approx -0.43$
• Point C (between 3 and 4, closer to 3): $\sqrt{12} \approx 3.46$
• Point D (between -4 and -3, closer to -3): $-\sqrt{10.24} = -3.2$
• Point E (between 3 and 4, closer to 4): $\sqrt{8} \approx 2.83$ *correction: $\sqrt{8} \approx 2.83$ is between 2 and 3, closer to 3; $\sqrt{12} \approx 3.46$ is between 3 and 4. Rechecking:
• Point A (1): $\sqrt{1.2} \approx 1.10$
• Point A revised: $\sqrt{1.2} \approx 1.10$ (matches point A at 1)
• Point (2): $\frac{19}{9} \approx 2.11$ (matches point between 2 and 3)
• Point C (3): $\sqrt{8} \approx 2.83$ (matches point between 2 and 3, closer to 3)
• Point E (4): $\sqrt{12} \approx 3.46$ (matches point between 3 and 4)
• Point B (0): $\frac{1}{8} = 0.125$ (matches point between 0 and 1, closer to 0)
• Point (0 left): $\sqrt{0.81} = 0.9$ (matches point between 0 and 1, closer to 1)
• Point F (-1): $-\frac{10}{7} \approx -1.43$ (matches point between -2 and -1, closer to -1)
• Point (-2): $-\frac{23}{9} \approx -2.56$ (matches point between -3 and -2, closer to -2)
• Point D (-3): $-\sqrt{10.24} = -3.2$ (matches point between -4 and -3, closer to -3)

Final precise matches:

• A: $\sqrt{1.2} \approx 1.10$
• B: $\frac{1}{8} = 0.125$
• C: $\sqrt{8} \approx 2.83$
• D: $-\sqrt{10.24} = -3.2$
• E: $\sqrt{12} \approx 3.46$
• F: $-\frac{10}{7} \approx -1.43$

Remaining values: $\sqrt{0.81}=0.9$ (matches point between 0 and 1, closer to 1), $\frac{19}{9}\approx2.11$ (matches point between 2 and 3, closer to 2), $-\frac{23}{9}\approx-2.56$ (matches point between -3 and -2, closer to -2), $-\frac{3}{7}\approx-0.43$ (matches point between -1 and 0, closer to 0)

Step3: Assign to labeled points

Based on number line positions:

• A (1): $\sqrt{1.2} \approx 1.10$
• B (0 right): $\frac{1}{8} = 0.125$
• C (3 left): $\sqrt{8} \approx 2.83$
• D (-3 left): $-\sqrt{10.24} = -3.2$
• E (3 right): $\sqrt{12} \approx 3.46$
• F (-1 left): $-\frac{10}{7} \approx -1.43$
• Unlabeled points:
• 0 left: $-\frac{3}{7} \approx -0.43$
• 0 right (close to 1): $\sqrt{0.81} = 0.9$
• 2 right: $\frac{19}{9} \approx 2.11$
• -2 left: $-\frac{23}{9} \approx -2.56$

Answer:

• A: $\boldsymbol{\sqrt{1.2} \approx 1.10}$
• B: $\boldsymbol{\frac{1}{8} = 0.125}$
• C: $\boldsymbol{\sqrt{8} \approx 2.83}$
• D: $\boldsymbol{-\sqrt{10.24} = -3.2}$
• E: $\boldsymbol{\sqrt{12} \approx 3.46}$
• F: $\boldsymbol{-\frac{10}{7} \approx -1.43}$

Remaining matches for unlabeled points:

• Between -1 and 0: $-\frac{3}{7} \approx -0.43$
• Between 0 and 1 (near 1): $\sqrt{0.81} = 0.9$
• Between 2 and 3 (near 2): $\frac{19}{9} \approx 2.11$
• Between -3 and -2 (near -2): $-\frac{23}{9} \approx -2.56$