(i)
Let
∴ x = 0.3333... ...(i)
10x = 3.3333... ...(ii)
On subtracting (i) from (ii), we get:
9x = 3
= x =
∴
(ii)
Let
∴ x = 1.3333... ...(i)
10x = 13.3333... ...(ii)
On subtracting (i) from (ii), we get:
9x = 12
= x =
∴
(iii)
Let x =
∴ x = 0.3434... ...(i)
100x = 34.3434... ...(ii)
On subtracting (i) from (ii), we get:
99x = 34
= x =
∴
(iv)
Let x =
∴ x = 3.1414... ...(i)
100x = 314.1414... ...(ii)
On subtracting (i) from (ii), we get:
99x = 311
= x =
∴ =
(v)
Let x =
∴ x = 0.324324... ...(i)
1000x = 324.324324... ...(ii)
On subtracting (i) from (ii), we get:
999x = 324
= x = =
∴ =
(vi)
Let x =
∴ x = 0.1777...
10x = 1.777... ...(i)
100x = 17.777.... ...(ii)
On subtracting (i) from (ii). we get:
90x = 16
= x =
∴ =
(vii)
Let x =
∴ x = 0.5444...
10x = 5.4444... ...(i)
100x = 54.4444... ...(ii)
On subtracting (i) from (ii), we get:
90x = 49
= x =
∴ =
(viii)
Let x =
∴ x = 0.16363...
10x = 1.6363... ...(i)
1000x = 163.6363... ...(ii)
On subtracting (i) from (ii), we get:
990x = 162
= x =
∴ =