Find the decimal representation of 1/7, 2/7. Deduce from the decimal representation of 1/7, without actual calculation, the decimal representation of 3/7, 4/7, 5/7 and 6/7.

9 Give an example for each, if two irrational numbers, whose
       (i) difference is a rational number.
       (ii) difference is a irrational number.
       (iii) sum is a rational number.
       (iv) sum is an irrational number.
       (v) product is an irrational number,
       (vi) product is an irrational number.
       (vii) quotient is a rational number.
       (viii) quotient is an irrational number. 10 Which of the following rational numbers have the terminating decimal representation?
       (i) 3/5              (ii) 7/20                   (iii) 2/13
       (iv) 27/40        (v) 133/125            (vi) 23/7
       [Making use of the result that a rational number p/q where p and q have no common factor(s) will have a terminating representation if and only if the prime factors of q are 2's or 5's or both.] 12 Express 0.6666………in the form of  13 If a and b are two rational numbers, prove that a + b, a - b, ab are rational numbers. If b ≠ 0, show that a/b is also a rational number.