The problem asks to convert the given fractions to decimal numbers and determine the type of decimal each represents (Periódico puro - pure periodic, Periódico mixto - mixed periodic, Exacto - exact).

1. Problem Description

The problem asks to convert the given fractions to decimal numbers and determine the type of decimal each represents (Periódico puro - pure periodic, Periódico mixto - mixed periodic, Exacto - exact).

2. Solution Steps

Fractions: $\frac{27}{4}$, $-\frac{17}{3}$, $-\frac{15}{8}$, $\frac{29}{6}$, $\frac{8}{3}$.

1. $\frac{27}{4}$:

Divide 27 by 4: $27 \div 4 = 6.75$. This is an exact decimal.

2. $-\frac{17}{3}$:

Divide 17 by 3: $17 \div 3 = 5.666... = 5.\overline{6}$. This is a pure periodic decimal (after the minus sign).

3. $-\frac{15}{8}$:

Divide 15 by 8: $15 \div 8 = 1.875$. This is an exact decimal (after the minus sign).

4. $\frac{29}{6}$:

Divide 29 by 6: $29 \div 6 = 4.8333... = 4.8\overline{3}$. This is a mixed periodic decimal.

5. $\frac{8}{3}$:

Divide 8 by 3: $8 \div 3 = 2.666... = 2.\overline{6}$. This is a pure periodic decimal.

3. Final Answer

Here's the solution:

* $\frac{27}{4} = 6.75$ (Exacto)

* $-\frac{17}{3} = -5.\overline{6}$ (Periódico puro)

* $-\frac{15}{8} = -1.875$ (Exacto)

* $\frac{29}{6} = 4.8\overline{3}$ (Periódico mixto)

* $\frac{8}{3} = 2.\overline{6}$ (Periódico puro)