By Michal Paszkiewicz.

Number - Structure and Calculation

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:

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:

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. \( 2 ^ {60} \)