Question

3. Express each of the following decimals in the form where p. 4 are
9
integers and q +0.0.2
G) 293 [2010, 15)​

Answer 1

Let x = bar 0.4 Now, x = bar 0.4 = 0.444.... ---(1) Multiplying both sides of equation (1) by 10, we get, 10x = 4.444.... --- (2) Subtracting equation (1) by (2) 10x - x = 4.444... -0.444... => 9x = 4 => x = 4/9 Hence, bar 0.4 = 4/9 (ii) Let x = bar 0.37 Now, x = 0.3737... .....(1) Multiplying equation (1) by l0. 10x = 3.737.... .......(2) 100 37.3737... ........(3) Subtracting equation (1) by equation (3) 100x - x = 37 => 99 x = 37 => x = 37/ 99 Hence,bar 0.37 = 37/ 99