The vulgar fraction of $${\text{0}}{\text{.39}}\overline {{\text{39}}} $$   is ?

The vulgar fraction of $${\text{0}}{\text{.39}}\overline {{\text{39}}} $$   is ? Correct Answer $$\frac{13}{33}$$

The given expression can be written in this form also
N = $${\text{ 0}}{\text{.39}}\overline {{\text{39}}} $$ ..... (i)
Multiply equation (i) with 100 on both sides.
100N = $${\text{39}}{\text{.}}\overline {{\text{39}}} $$ ..... (ii)
Subtracting equation (i) from (ii) we get,
⇒ 100N - N = $${\text{39}}\overline {{\text{.39}}} $$  - $${\text{0}}\overline {{\text{.39}}} $$
⇒ 99N = 39
⇒ N = $$\frac{39}{99}$$ = $$\frac{13}{33}$$