Find the rational number whose decimal expansion is given below :

(i) (ii)

(iii)

(i) Let, x=0.3333…

⇒ x=0.3+0.03+0.003+…

⇒ x=3(0.1+0.01+0.001+0.0001+…∞)

⇒ x=3()

This is an infinite geometric series.

Here, a=1/10 and r=1/10

∴x

₌

(ii) _{Let, x=0.231231231….}

_{⇒ x=0.231+0.000231+0.000000231+…∞}

⇒ x=231(0.001+0.000001+0.000000001+…∞)

⇒ x=231(++…∞)

This is an infinite geometric series.

Here, a and r=

⇒

₌

(iii) Let, x=3.525252552…

⇒ x=3+0.52+0.0052+0.000052+…∞

⇒ x=3+52(0.01+0.0001+…∞)

⇒ x=3+52(++…∞)

Here, a and r=

⇒