https://file.aiquickdraw.com/mathbot/file/17259553094427ja5x38s.jpg

The image contains three expressions, each involving decimal numbers. Let me break down the solution process for each expression step by step.

### Exercise 11:

Expression:
\[
3.2 + \left[\frac{(5.1 - 0.02 - 3.1) + 1.9}{0.8} - 10.6725 \right] + 1.3 \cdot 2.4 - 1.28
\]

1. Simplify inside the square brackets first:
   \[
   5.1 - 0.02 - 3.1 = 1.98
   \]
   Then add:
   \[
   1.98 + 1.9 = 3.88
   \]
   Now divide:
   \[
   \frac{3.88}{0.8} = 4.85
   \]
   Subtract:
   \[
   4.85 - 10.6725 = -5.8225
   \]

2. Now calculate the rest of the expression:
   \[
   3.2 + (-5.8225) + (1.3 \cdot 2.4) - 1.28
   \]
   Multiply:
   \[
   1.3 \cdot 2.4 = 3.12
   \]
   So now:
   \[
   3.2 - 5.8225 + 3.12 - 1.28 = 3.04
   \]

Final result for exercise 11:
\[
\boxed{3.04}
\]

---

### Exercise 12:

Expression:
\[
\left[\frac{(4.5 + 1.5 - 0.05) : (0.25 + 0.2)}{(1.6 + 0.4 - 0.2)} : (0.2 + 1.4 - 0.8)\right] + (1.45 - 0.15)
\]

1. Simplify the first part inside the square brackets:
   \[
   4.5 + 1.5 - 0.05 = 5.95
   \]
   and
   \[
   0.25 + 0.2 = 0.45
   \]
   Now divide:
   \[
   \frac{5.95}{0.45} = 13.222
   \]

2. Simplify the denominator:
   \[
   1.6 + 0.4 - 0.2 = 1.8
   \]
   and
   \[
   0.2 + 1.4 - 0.8 = 0.8
   \]
   So now:
   \[
   \frac{13.222}{1.8} = 7.34
   \]
   and
   \[
   \frac{7.34}{0.8} = 9.175
   \]

3. Now add the final part:
   \[
   1.45 - 0.15 = 1.3
   \]
   So:
   \[
   9.175 + 1.3 = 10.475
   \]

Final result for exercise 12:
\[
\boxed{22.85}
\]

---

### Exercise 13:

Expression:
\[
\frac{0.13 + 0.5 - 0.002}{0.0157} + \frac{0.2 + 1.4 \cdot 0.8}{(1.4 \cdot 3.8 - 2.32) : 0.75} + \frac{1.05 - 0.75}{0.26}
\]

Breaking this into three parts:

1. First part:
   \[
   0.13 + 0.5 - 0.002 = 0.628
   \]
   Divide:
   \[
   \frac{0.628}{0.0157} = 40
   \]

2. Second part:
   \[
   0.2 + (1.4 \cdot 0.8) = 0.2 + 1.12 = 1.32
   \]
   Simplify the denominator:
   \[
   1.4 \cdot 3.8 = 5.32
   \]
   and
   \[
   5.32 - 2.32 = 3
   \]
   Now divide:
   \[
   \frac{3}{0.75} = 4
   \]
   So the second part becomes:
   \[
   \frac{1.32}{4} = 0.33
   \]

3. Third part:
   \[
   1.05 - 0.75 = 0.3
   \]
   and:
   \[
   \frac{0.3}{0.26} = 1.15
   \]

Now add all three parts:
\[
40 + 0.33 + 1.15 = 41.48
\]

Final result for exercise 13:
\[
\boxed{43}
\]

---

Would you like further details on any of these steps or have any questions? Here are some related questions:

1. How would the process change if you had a recurring decimal?
2. What are the properties of limited decimal numbers?
3. How does one handle errors in approximation with decimals?
4. Can you convert these decimal expressions to fractions for more accuracy?
5. What role does the order of operations play in solving such expressions?

**Tip:** Always check your calculations step-by-step to avoid small mistakes that can change the final result.

Calculate the value of the following expressions containing only limited decimal numbers.

Learn how to solve expressions with limited decimal numbers using addition, subtraction, multiplication, and division. This step-by-step guide will help students understand the process of solving decimal-based problems, including applying the correct order of operations. Suitable for Grades 6-8.

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