Express each of the following decimals in the form pq :
(i) 0.¯¯¯4 (ii) 0.¯¯¯¯¯¯37
(i) 0.¯¯¯4
Let x = 0.¯¯¯4 = 0.4444.... ....(i)
10 x = 4.4444... ....(ii)
Subtracting (i) from (ii)
9x = 4 ⇒ x = 49
∴0.¯¯¯4=49
(ii) 0.¯¯¯¯¯¯37
Let x = 0.¯¯¯¯¯¯37 = 0.373737... ....(i)
100 x = 37.373737... ....(ii)
Subtracting (i) from (ii)
99 x = 37 ⇒ x = 3799
∴ 0.¯¯¯¯¯¯37 = 3799