https://r2.erweima.ai/mathbot/image/1725977727834by1zbea3.jpg

Let's break down and solve both sets of exercises shown in the image.

### 1. **First Task: Convert to a Decimal (Wandle in eine Dezimalzahl um)**

You are asked to convert fractions into their decimal equivalents. Here's how we can do it:

#### a) \( \frac{3}{8} \)
Divide 3 by 8:
\[
\frac{3}{8} = 0.375
\]

#### b) \( \frac{9}{11} \)
Divide 9 by 11:
\[
\frac{9}{11} = 0.\overline{81} \quad \text{(a repeating decimal)}
\]

#### c) \( \frac{14}{27} \)
Divide 14 by 27:
\[
\frac{14}{27} = 0.\overline{518} \quad \text{(a repeating decimal)}
\]

#### d) \( \frac{27}{44} \)
Divide 27 by 44:
\[
\frac{27}{44} \approx 0.6136 \quad \text{(a finite decimal)}
\]

#### e) \( \frac{127}{44} \)
Divide 127 by 44:
\[
\frac{127}{44} \approx 2.886 \quad \text{(a finite decimal)}
\]

### 2. **Second Task: Convert to a Fraction (Wandle in einen Bruch um)**

Now, we will convert the given decimals into fractions.

#### a) \( 0.254 \)
This is a finite decimal:
\[
0.254 = \frac{254}{1000} = \frac{127}{500}
\]

#### b) \( 0.13 \)
This is also a finite decimal:
\[
0.13 = \frac{13}{100}
\]

#### c) \( 1.\overline{4} \)
This is a repeating decimal:
\[
1.\overline{4} = \frac{14}{9}
\]

#### d) \( 2.023 \)
This is a finite decimal:
\[
2.023 = \frac{2023}{1000}
\]

#### e) \( 0.0012 \)
This is also a finite decimal:
\[
0.0012 = \frac{12}{10000} = \frac{3}{2500}
\]

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Let me know if you need any further explanation on these steps. 

### Additional Questions to Explore:
1. How would you handle converting a mixed number to a decimal or fraction?
2. What is the process to convert a repeating decimal into a fraction?
3. What are some common patterns in repeating decimals and their fraction equivalents?
4. How can you estimate the value of a fraction without using a calculator?
5. Why do some decimals terminate while others repeat infinitely?

**Tip**: When converting repeating decimals to fractions, a helpful trick is to multiply the decimal by powers of 10 to isolate the repeating part.

Solve problems converting fractions like 3/8 and 9/11 to decimals, and decimals like 0.254 and 1.4 to fractions. Learn step-by-step how to handle repeating and finite decimals, suitable for Grades 6-8.

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