Question

express 0.23232.....in the form of p/q, qis not equal to zero and find the value of p+q/q-p​

Answer 1

$Let \: x = 0.232323\ldots \: ---(1)$

/* Multiplying equation (1) by 100, we get */

$100x = 23.232323\ldots \: ---(2)$

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

$99x = 23$

$\implies x = \frac{23}{99}\: \blue{ (\frac{p}{q} \: form )}$

$p = 23 \: and \: q = 99$

Therefore.,

$\red{ Value \: of \: \frac{p+q}{q-p} }$

$= \frac{23 + 99}{99-23}$

$= \frac{ 122}{76}$

$\green {= \frac{61}{38} }$

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