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=





1