By Michal Paszkiewicz.

# Number - Structure and Calculation

**Please do not use a calculator!**
Try all the questions, but if you struggle with one too much, move on to the next one.

### 1. Put these numbers in order from lowest to highest:

\( \frac{355}{113} \), 4, \( \frac{22}{7} \), \( \frac{333}{106} \), 3.5, \( \frac{38}{13} \), \( \frac{19}{6} \), 3

### 2. Calculate the following:

$$ \frac{\frac{12}{5} \times 15}{12} \div \frac{3}{10} $$
Read about the divisibility rules from 1 to 16 found here.

### 3. Write in your own words an easy way of figuring out whether a big number can be divided by these numbers:

- 4
- 9
- 16
- 25

### 4. Simplify the following surds:

- \( \sqrt{52} \)
- \( \sqrt{425} \)
- \( \sqrt{171} \)
- \( \sqrt{225} \)
- \( \sqrt{208 \pi} \)
- \( \sqrt{25200} \)
- \( \sqrt[3]{40} \)

### 5. Calculate the following and present it in the format \( A \times 10^n \) where \( 1 \leq A < 10 \)

Answers do not have to be given to more than 3 significant figures

- \( 2 ^ 3 \)
- \( 2 ^ 5 \)
- \( 2 ^ {10} \)
- \( 2 ^ {20} \)
- \( 2 ^ {30} \)
- \( 2 ^ {60} \)