Find three different irrational numbers between the rational numbers 5/7 and 9/11

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

Write three numbers whose decimal expansions are non-terminating non-recurring.

Classify the following numbers as rational or irrational:

(i)

(ii)

(iii) 0.3796

(iv) 7.478478…

(v) 1.101001000100001….

Visualize 3.765 on the number line, using successive magnification.