IaPressExpress in p by Q form 0.36

1.	IaPressExpress in p by Q form 0.36
Answer» 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 $\it <klux>X</klux>$ . $\rm \implies x = 0.\overline{36}$ 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: $\sf {\therefore Thus, \: 0.\overline{36} \: is \: in \: the \: form \: of \: \dfrac{p}{q} \: where \: p = 4 \: and \: q = 11.}$

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