Question

Express 5. Bar 2 in form p/q

Answer 1

$Let \: x = 5.\overline 2$

$\implies x = 5.2222\cdot\cdot\cdot \:---(1)$

/* Multiplying equation (1) by 10, we get */

$\implies 10x = 52.5.2222\cdot\cdot\cdot \:---(2)$

/* Subtract Equation (1) from Equation (2) , we get*/

$\implies 9x = 47$

$\implies x = \frac{47}{9} \: \pink { (\frac{p}{q} \:form) }$

Therefore.,

$\red { 5.\overline 2}\green { = \frac{47}{9} \: \pink { (\frac{p}{q} \:form) ) }}$

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