What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\dfrac{1}{17}$ ? Perform the division to check your answer.

Look at several examples of rational numbers in the form $\dfrac{p}{q}$ (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Find three different irrational numbers between the rational numbers $\dfrac{5}{7}$ and $\dfrac{9}{11}$ .

Classify the following numbers as rational or irrational :

(i) $\sqrt{23}$

(ii) $\sqrt{225}$

(iii) 0.3796

(iv) 7.478478…

(v) 1.101001000100001…