QUESTION 1 1.1 State whether each of the following numbers are rational, irrational or neither $$ 1.1 .1 \sqrt{2 \frac{2}{2}} $$ $$ 1.1 .2 \frac{\pi}{4} $$ 1.1 .387 1.2 Write 0.32 in the form of $$ \frac{a}{b} $$, where $$ a $$ and $$ b $$ are integers. Show all your workings

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**1.1.1**  
We start with  
$$
\sqrt{2 \frac{2}{2}}
$$  
First, interpret the mixed number $$2 \frac{2}{2}$$. This equals  
$$
2 + \frac{2}{2} = 2 + 1 = 3.
$$  
Thus, the expression becomes  
$$
\sqrt{3}.
$$  
Since $$3$$ is not a perfect square, $$\sqrt{3}$$ is an irrational number.

---

**1.1.2**  
Consider the number  
$$
\frac{\pi}{4}.
$$  
We know that $$\pi$$ is irrational. Multiplying or dividing an irrational number by a nonzero rational number (here, $$\frac{1}{4}$$) yields an irrational number. Hence, $$\frac{\pi}{4}$$ is irrational.

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**1.1.387**  
The number $$387$$ is an integer. Every integer can be expressed as a fraction (for example, $$387 = \frac{387}{1}$$), so it is a rational number.

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**1.2**  
We need to express $$0.32$$ in the form  
$$
\frac{a}{b},
$$  
where $$a$$ and $$b$$ are integers.

1. Write $$0.32$$ as a fraction over $$100$$:
   $$
   0.32 = \frac{32}{100}.
   $$
2. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is $$4$$:
   $$
   \frac{32}{100} = \frac{32 \div 4}{100 \div 4} = \frac{8}{25}.
   $$

Thus, $$0.32$$ in the form $$\frac{a}{b}$$ is  
$$
\frac{8}{25}.
$$
**1.1.1** $$\sqrt{2 \frac{2}{2}}$$ is irrational. **1.1.2** $$\frac{\pi}{4}$$ is irrational. **1.1.387** 387 is rational. **1.2** $$0.32 = \frac{8}{25}$$.

QUESTION 1 1.1 State whether each of the following numbers are rational, irrational or neither \( 1.1 .1 \sqrt{2 \frac{2}{2}} \) \( 1.1 .2 \frac{\pi}{4} \) 1.1 .387 1.2 Write 0.32 in the form of \( \frac{a}{b} \), where \( a \) and \( b \) are integers. Show all your workings

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