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

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UpStudy AI · Accepted Answer

To determine which of the given expressions are rational numbers, let's analyze each one:

1. **$$\frac{-5}{0}$$**
   - **Undefined**: Division by zero is not defined in mathematics.
   - **Not a rational number**.

2. **$$\frac{0}{0}$$**
   - **Undefined**: This expression is indeterminate and has no defined value.
   - **Not a rational number**.

3. **$$0.11\overline{1}$$**
   - **Repeating Decimal**: This represents the number $$0.1111\ldots$$, which is equal to $$\frac{1}{9}$$.
   - **Rational number**.

4. **$$\frac{0}{-10}$$**
   - **Simplifies to 0**: Any number divided by a non-zero number is 0.
   - **Rational number**.

5. **$$\sqrt{2}$$**
   - **Irrational Number**: $$\sqrt{2}$$ cannot be expressed as a fraction of two integers.
   - **Not a rational number**.

6. **$$\frac{2}{-2}$$**
   - **Simplifies to -1**: This is a simple division resulting in -1.
   - **Rational number**.

7. **$$\sqrt{36}$$**
   - **Simplifies to 6**: Since $$\sqrt{36} = 6$$, which is an integer.
   - **Rational number**.

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

**Therefore, the rational numbers are:**

- $$0.11\overline{1}$$
- $$\frac{0}{-10}$$
- $$\frac{2}{-2}$$
- $$\sqrt{36}$$
The rational numbers are $$0.11\overline{1}$$, $$\frac{0}{-10}$$, $$\frac{2}{-2}$$, and $$\sqrt{36}$$.

Choose all of the rational numbers.

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