Let’s break down and solve the exercise step by step based on the image you provided.

The task is to:

1. Identify if each number is exact, repeating (periodic), or semi-repeating (semiperiodic).
2. Convert each number to its equivalent fraction.

The list of numbers to work with is:

1. $0.6$
2. $1.454545\ldots$
3. $3.025$
4. $2.5$
5. $0.8333\ldots$
6. $4.181818\ldots$
7. $0.090909\ldots$
8. $5.0125$

Solutions:

1. $0.6$:

   • Type: Exact decimal (terminates).
   • Fraction: $0.6 = \frac{6}{10} = \frac{3}{5}$.

2. $1.454545\ldots$:

   • Type: Repeating decimal.
   • Fraction: $1.454545\ldots = 1 + 0.454545\ldots$. To convert the repeating part $0.454545\ldots$, let: $x = 0.454545\ldots$ Multiply by 100 to shift the decimal: $100x = 45.454545\ldots$ Subtract the original equation: $100x - x = 45.454545\ldots - 0.454545\ldots$ This gives: $99x = 45 \implies x = \frac{45}{99} = \frac{5}{11}$ Therefore: $1.454545\ldots = 1 + \frac{5}{11} = \frac{16}{11}$

3. $3.025$:

   • Type: Exact decimal (terminates).
   • Fraction: $3.025 = \frac{3025}{1000} = \frac{605}{200} = \frac{121}{40}$.

4. $2.5$:

   • Type: Exact decimal (terminates).
   • Fraction: $2.5 = \frac{25}{10} = \frac{5}{2}$.

5. $0.8333\ldots$:

   • Type: Repeating decimal.
   • Fraction: $0.8333\ldots = \frac{5}{6}$ (this is a known repeating decimal).

6. $4.181818\ldots$:

   • Type: Repeating decimal.
   • Fraction: $4.181818\ldots = 4 + 0.181818\ldots$. Let: $y = 0.181818\ldots$ Multiply by 100: $100y = 18.181818\ldots$ Subtracting the original equation: $100y - y = 18.181818\ldots - 0.181818\ldots$ This gives: $99y = 18 \implies y = \frac{18}{99} = \frac{2}{11}$ Therefore: $4.181818\ldots = 4 + \frac{2}{11} = \frac{46}{11}$

7. $0.090909\ldots$:

   • Type: Repeating decimal.
   • Fraction: $0.090909\ldots = \frac{1}{11}$.

8. $5.0125$:

   • Type: Exact decimal (terminates).
   • Fraction: $5.0125 = \frac{50125}{10000} = \frac{802}{160} = \frac{401}{80}$.

Let me know if you'd like more details on any of the steps. Here are five related questions to deepen your understanding:

1. How do you convert a repeating decimal into a fraction?
2. What is the difference between exact and repeating decimals?
3. Can a semiperiodic decimal always be converted to a simple fraction?
4. What methods exist to simplify complex fractions?
5. How does the position of the repeating part in a decimal affect the conversion process?

Tip: Always check if a fraction can be simplified after converting a decimal. This ensures that the fraction is in its lowest terms.