Question

Solve this question from the image ​

Answer 1

ANSWER:

To Do:

• Express $\sf0.\overline{36}$ in p/q form

Solution:

We are given that,

$\implies\sf0.\overline{36}$

Let this be equal to x.

So,

$\implies\sf x=0.\overline{36}- - - -(1)$

Multiplying both side by 100,

$\implies\sf 100x=36.\overline{36}- - - -(2)$

Subtracting (2) from (1),

$\implies\sf 100x-x=36.\overline{36}-0.\overline{36}$

$\implies\sf 99x=36$

So,

$\implies\sf x=\dfrac{36}{99}$

Dividing by 9,

$\implies\sf x=\dfrac{4}{11}$

Hence,

$\implies\bf0.\overline{36}=\dfrac{4}{11}$

Therefore, option D) is correct.