3. Express the following in the form are integers and q ! 0 :(i) 0.6 (ii) 0.47Sol :qp , where p and q(iii) 0.001

(i) 0.6 Let x = 0.6 or x = 0.666 .......... ...(1) Multiplying eq (1) by 10 we have 10x = 6.666 .......... ...(2) Subtracting eq (1) from (2) we have 9x = 6 Hence, x = 2 3 (ii) 0.47 Let x = 0.47 or x = 0.4777 .......... ...(1) Multiplying eq (1) by 10 we have 10x = 4.777 .......... ...(2) Again multiplying eq (2) by 10, we get 100x = 47.777 .......... ...(3) Subtracting equation (2) from equation (3), we get 90x = 43 Hence, x = 43 90 (iii) 0.001 Let x = 0.001 or x = 0.001001 .......... ...(1) Multiplying eq (1) by 1000 we have 1000x = 1.001001 .......... ...(2) Subtracting (1) from (2) we have 999x = 1 Hence, x = 1 999