Question

IaPressExpress in p by Q form 0.36 ​

Answer 1

Correct Question:

Express  $0.\overline{36}$ in the form of p/q.

Given:

A number -

• $0.\overline{36}$

What To Find:

We have to -

• Express in the form of p/q.

Solution:

Let us take $0.\overline{36}$ as $\it x$.

$\rm \implies x = 0.\overline{36}$

Multiply 100 on both sides,

$\rm \implies 100 \times x = 100 \times 0.3636...$

Multiply,

$\rm \implies 100x = 36.3636...$

If we take it as,

$\rm \implies 100x = 36 + 0.3636...$

We know that x = 0.3636...

$\rm \implies 100x = 36 + x$

Take x to LHS,

$\rm \implies 100x - x = 36$

Subtract x from 100x,

$\rm \implies 99x = 36$

Take 99 to RHS,

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

Simplify the number,

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

Final Answer:

$\sf {\therefore Thus, \: 0.\overline{36} \: is \: in \: the \: form \: of \: \dfrac{p}{q} \: where \: p = 4 \: and \: q = 11.}$