Question

Express 8.2353535…. as a rational number, in the simplest P/Q form where p & q are integers and q ≠ 0
'himmat hai to solve karo'

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Answer 1

$Let \: x = 8.2353535\ldots \: --(1)$

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

$\implies 10x = 82.353535\ldots \: --(2)$

/* Multiplying equation (2) by 100 , we get */

$\implies 1000x = 8235.253535\ldots \: ---(3)$

/* Subtract equation (2) from equation (3) , we get */

$\implies 990x = 8153$

$\implies x = \frac{8153}{990} \: \blue{ ( \frac{p}{q} \:form ) }$

Therefore.,

$\red{ 8.2353535\ldots } \green {= \frac{8153}{990} \: \blue{ ( \frac{p}{q} \:form ) }}$

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