Let's go through the questions from the worksheet in your image one by one:

1. Absolute Value Problems:

   • The first three problems ask to find the absolute value of each number:
     1. $|-9.8|$ → The absolute value is $9.8$.
     2. $|12 \frac{1}{3}|$ → The absolute value is $12 \frac{1}{3}$.
     3. $|-2 \frac{9}{10}|$ → The absolute value is $2 \frac{9}{10}$.

2. Comparison of Absolute Values: In questions 4–6, you are asked to compare the absolute values using $<$, $>$, or $=$: 4. Compare $|0.95|$ and $|-1.5|$:

   • Absolute value of $0.95 = 0.95$
   • Absolute value of $-1.5 = 1.5$
   • $0.95 < 1.5$ (This seems correct, and you marked it that way.)

   5. Compare $|-10.1|$ and $|10 \frac{3}{20}|$:

      • Absolute value of $-10.1 = 10.1$
      • Absolute value of $10 \frac{3}{20} = 10.15$
      • $10.1 < 10.15$ (You answered this correctly.)

   6. Compare $|-3.4|$ and $|-4|$:

      • Absolute value of $-3.4 = 3.4$
      • Absolute value of $-4 = 4$
      • $3.4 < 4$ (Correct answer as well.)

3. Plotting on the Number Line:

   • Noah needs to plot the number $-|9|$ on the number line. Since $|9| = 9$, $-|9| = -9$. Noah should plot the point at $-9$, which is marked correctly.

4. Multiple-Choice Question (Question 8):

   • This question asks which statement is not true about $-6.7$.
   • You marked choice C: "The absolute value of the number is positive."
     • This is true because absolute values are always positive.
     • The incorrect answer here should be choice D: "The number is 6.7 units away from zero." That is a true statement. So, C is correctly marked.

5. Real-World Situations (Question 9):

   • You were asked to represent the following real-world situations with an integer:
     • (a) The temperature drops to $15$ degrees below zero:
       • The integer is $-15$, and the absolute value representing the change is $|-15| = 15$.
     • (b) Michael's account goes from $0 to $-75$ after a purchase:
       • The integer is $-75$, and the absolute value is $|-75| = 75$.
     • (c) An elevator rises to the ninth floor:
       • The integer is $9$, and the absolute value is $|9| = 9$.
     • (d) The parking garage is 4 floors underground:
       • The integer is $-4$, and the absolute value is $|-4| = 4$.

Everything seems to be mostly correct on your worksheet. You got 5/12, but some answers seem fine. Perhaps more detailed checking by the teacher led to these marks.

Would you like more details on any of these problems or have any questions?

Here are five related questions for further practice:

1. What is the absolute value of $-\frac{7}{4}$?
2. Compare the absolute values: $|5.3|$ vs. $|-4.9|$.
3. Plot $-|6|$ on a number line.
4. Which of the following is false? The absolute value of a positive number is always positive.
5. How does absolute value relate to real-world measurements, such as distance or temperature changes?

Tip: Absolute value can be thought of as the "distance" from zero, which is always a positive quantity.