Express each of the following decimals in the form p/ q: (i) 0. 4̅ (ii) 0.37 bar

Question

Express each of the following decimals in the form p/q :

(i) 0. 4̅   

(ii) bar 0.37

Answer 1

(i) 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