Question

$\huge\underline\mathbb\red{QUESTION}$
$0.\bar{3}\bar{6} \: \: in \: \: \frac{p}{q} \: \: form \: \: is \:$

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Answer 1

Answer

0.363636.. = ⁴/₁₁

Given

$\rm \bullet \;\; 0.\overline{36}$

To Find

$\rm \bullet \;\; \dfrac{p}{q}\ form\ of\ 0.\overline{36}$

Solution

Let us assume that ,

 x = $0.\overline{36}$

⇒ x = 0.363636... (1)

Multiply this eq(1) with 100 ,

⇒ 100x = 36.363636... (2)

Now , Solve (2) - (1) ,

⇒ 100x - x = 36.363636.. - 0.363636..

⇒ 99x = 36

⇒ x = ⁴/₁₁

So , p/q form , x = ⁴/₁₁

Answer 2

Let ,

x = 0.3636 ... --- (i)

Multiply eq (i) by 100 , we get

100x = 36.3636 --- (ii)

Subtract eq (i) from eq (ii) , we get

100x - x = 39.3636 ... - 0.3636 ...

99x = 36

x = 36/99

x = 4/11

$\therefore$ 0.3636 ... in p/q form is 4/11