5.1 Indicate whather eatah of the lol owing numbers is rational or irmiloant 0,$$ 8 ; \quad 2 \frac{1}{6} ; \pi ;-\sqrt{3} $$ 5.2 Arrange in asconding oroer $$ \sqrt{3} ; \quad \sqrt[3]{2} ; \quad \sqrt[4]{2} ; \sqrt{2} $$ atter 5.3 On a number line, indicate between which two integers $$ \sqrt{7} $$ lies. 5.4 Round 943,738095 to 2 decumal places. 5.5 Convert 0.5 to a common frection (3)

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Sure, let's tackle each of these problems step by step.

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### **5.1 Indicate Whether Each of the Following Numbers Is Rational or Irrational**

**a) 0.8**

- **Rational**
  
  **Explanation:**  
  0.8 can be expressed as the fraction $$ \frac{8}{10} $$, which simplifies to $$ \frac{4}{5} $$. Since it can be written as a ratio of two integers, it is rational.

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**b) $$ 2 \frac{1}{6} $$**

- **Rational**  
   
  **Explanation:**  
  $$ 2 \frac{1}{6} $$ can be converted to an improper fraction:  
  $$ 2 \frac{1}{6} = \frac{13}{6} $$.  
  This is a ratio of two integers, so it is rational.

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**c) $$ \pi $$**

- **Irrational**  
   
  **Explanation:**  
  $$ \pi $$ cannot be expressed as a ratio of two integers. Its decimal expansion is non-repeating and infinite, making it irrational.

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**d) $$ -\sqrt{3} $$**

- **Irrational**  
   
  **Explanation:**  
  $$ \sqrt{3} $$ is known to be irrational, and multiplying it by -1 does not change its irrationality. Therefore, $$ -\sqrt{3} $$ is also irrational.

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### **5.2 Arrange in Ascending Order**

**Numbers to Arrange:**  
$$ \sqrt{3} $$, $$ \sqrt[3]{2} $$, $$ \sqrt[4]{2} $$, $$ \sqrt{2} $$

**Approximate Decimal Values:**

- $$ \sqrt[4]{2} \approx 1.1892 $$
- $$ \sqrt[3]{2} \approx 1.2599 $$
- $$ \sqrt{2} \approx 1.4142 $$
- $$ \sqrt{3} \approx 1.7320 $$

**Ascending Order:**  
$$ \sqrt[4]{2} < \sqrt[3]{2} < \sqrt{2} < \sqrt{3} $$

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### **5.3 On a Number Line, Indicate Between Which Two Integers $$ \sqrt{7} $$ Lies**

**Solution:**  
- $$ 2^2 = 4 $$
- $$ 3^2 = 9 $$

Since $$ 4 < 7 < 9 $$, it follows that:
$$ 2 < \sqrt{7} < 3 $$

**Conclusion:**  
$$ \sqrt{7} $$ lies **between 2 and 3** on the number line.

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### **5.4 Round 943.738095 to 2 Decimal Places**

**Step-by-Step Rounding:**

1. **Identify the Third Decimal Place:**  
   - The number is 943.738095.
   - The third decimal digit is **8**.

2. **Determine Whether to Round Up:**  
   - Since the third decimal digit (**8**) is greater than or equal to 5, we round up the second decimal digit.

3. **Perform the Rounding:**  
   - The second decimal digit is **3**.  
   - Adding 1 gives **4**.

**Rounded Number:**  
$$ 943.74 $$

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### **5.5 Convert 0.5 to a Common Fraction**

**Solution:**  
$$ 0.5 = \frac{1}{2} $$

**Conclusion:**  
0.5 as a common fraction is $$ \frac{1}{2} $$.

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I hope this helps! Let me know if you have any further questions.
**5.1 Indicate Whether Each Number Is Rational or Irrational** - **0.8:** Rational - **2 1/6:** Rational - **π:** Irrational - **-√3:** Irrational **5.2 Arrange the Numbers in Ascending Order** $$ \sqrt[4]{2} < \sqrt[3]{2} < \sqrt{2} < \sqrt{3} $$ **5.3 $$ \sqrt{7} $$ Lies Between 2 and 3** **5.4 Rounded to 2 Decimal Places:** 943.74 **5.5 0.5 as a Fraction:** $$ \frac{1}{2} $$

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