Choose all of the rational numbers. $$ \frac{-5}{0} $$ $$ \frac{0}{0} $$ $$ 0.11 \overline{1} $$ $$ \frac{0}{-10} $$ $$ \sqrt{2} $$ $$ \frac{2}{-2} $$ $$ \sqrt{36} $$

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To determine which of the provided numbers are rational, let's evaluate each one:

1. **$$\frac{-5}{0}$$**: Division by zero is undefined, so this is **not** a rational number.

2. **$$\frac{0}{0}$$**: This is an indeterminate form and is **not** a rational number.

3. **$$0.11\overline{1}$$**:
   - This represents a repeating decimal: $$0.1111\ldots$$, which can be expressed as the fraction $$\frac{1}{9}$$.
   - Since it can be written as a ratio of two integers, it **is** a rational number.

4. **$$\frac{0}{-10}$$**:
   - This simplifies to $$0$$.
   - Zero is a rational number because it can be expressed as $$\frac{0}{1}$$.
   
5. **$$\sqrt{2}$$**:
   - $$\sqrt{2}$$ is an irrational number, meaning it cannot be expressed as a ratio of two integers.
   
6. **$$\frac{2}{-2}$$**:
   - This simplifies to $$-1$$.
   - Since $$-1$$ is an integer, it **is** a rational number.

7. **$$\sqrt{36}$$**:
   - $$\sqrt{36} = 6$$, which is an integer.
   - Integers are rational numbers because they can be expressed as a ratio (e.g., $$\frac{6}{1}$$).

**Rational Numbers from the List:**
- $$0.11\overline{1}$$
- $$\frac{0}{-10}$$
- $$\frac{2}{-2}$$
- $$\sqrt{36}$$

**Answer:**
All of the following are rational:
 $$0.11 \overline{1}$$,
 $$\frac{0}{-10}$$,
 $$\frac{2}{-2}$$, and
 $$\sqrt{36}$$.
The rational numbers from the list are: - $$0.11\overline{1}$$ - $$\frac{0}{-10}$$ - $$\frac{2}{-2}$$ - $$\sqrt{36}$$

Choose all of the rational numbers. \( \frac{-5}{0} \) \( \frac{0}{0} \) \( 0.11 \overline{1} \) \( \frac{0}{-10} \) \( \sqrt{2} \) \( \frac{2}{-2} \) \( \sqrt{36} \)

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