# 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:

$$\frac{\frac{12}{5} \times 15}{12} \div \frac{3}{10}$$

1. 4
2. 9
3. 16
4. 25

### 4. Simplify the following surds:

1. $$\sqrt{52}$$
2. $$\sqrt{425}$$
3. $$\sqrt{171}$$
4. $$\sqrt{225}$$
5. $$\sqrt{208 \pi}$$
6. $$\sqrt{25200}$$
7. $$\sqrt[3]{40}$$

### 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

1. $$2 ^ 3$$
2. $$2 ^ 5$$
3. $$2 ^ {10}$$
4. $$2 ^ {20}$$
5. $$2 ^ {30}$$
6. $$2 ^ {60}$$