Express the following in the form of where p and q are integers and q ≠ 0.

i. 0.3

ii.

iii.

iv.

i. 0.3

=

ii.

Let x = = 0.47474747… ..(i)

Multiplying equation (i) with 100. We get,

100x = 47.4747474.. ..(ii)

Subtracting (ii) for (i) i.e. (ii) – (i). We get,

99x = 47

x =

Thus,

iii.

Let x = = 1.27272727… ..(i)

Multiplying equation (i) with 100. We get,

100x = 127.27272727.. ..(ii)

Subtracting (ii) for (i) i.e. (ii) – (i). We get,

99x = 126

x =

Thus,

iv.

Let x = = 1.2353535… ..(i)

Multiplying equation (i) with 10. We get,

10x = 12.353535.. ..(ii)

Multiplying equation (i) with 1000. We get,

1000x = 1235.3535.. ..(iii)

Subtracting (iii) for (ii) i.e. (iii) – (ii). We get,

990x = 1223

x =

Thus,