State whether the following statements are true or false. Give reasons for your answers. (i) Number of rational numbers between 15 and 18 are finite. (ii) There are numbers which cannot be written in the form , where p and q both are integers and q ≠ 0. (iii) Decimal representation of rational numbers cannot be non-terminating non-repeating. (iv) The product of any two irrational numbers is always irrational.

Step-by-step solution

(i) False, because infinite rational numbers can be inserted between any two rational numbers. (ii) True, yes we can insert infinite rational and irrational numbers between two integers. But irrational numbers cannot be written in the form , where p and q both are integers and q ≠ 0. (iii) True. This is because decimal expansion of a rational number is either terminating or nonterminating recurring, i.e. repeating. (iv) This is not compulsory. For example, (Rational) But (Irrational)