Question

prove that the recurring decimal 0.39 =13/33

Answer 1

suppose, recurring decimal 0.39 = X ; where X = required real no.

we can write recurring decimal 0.39 as 0.3939...

then,

0.3939...=X

3.939.....=10X

3+0.93...=10X

0.939....=10X -3

then,

0.3939...=X

393.93...=1000X

393+0.939..= 1000X

0.9393...= 1000X -393

or, 10X - 3=1000X - 393

or, 393-3 = 1000X -10X

or, 390 = 990X

or, X = 390/990

or, X = 13/33

HENCE PROVEN