The vulgar fraction of $${\text{0}}{\text{.39}}\overline {{\text{39}}} $$ is ?
Options:
A . $$\frac{15}{33}$$
B . $$\frac{11}{39}$$
C . $$\frac{17}{39}$$
D . $$\frac{13}{33}$$
Answer: Option D 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 = $$\frac{39}{99}$$ = $$\frac{13}{33}$$
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