Question

the value of 0.23bar +0.22bar

Answer 1

hlo
see the pic which I have attached

Answer 2

$i )Let \:x= 0.\overline{23}$

$\implies x = 0.232323.\cdot\cdot\cdot\:--(1)$

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

$\implies 100x = 23.2323.\cdot\cdot\cdot\:--(2)$

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

$\implies 99x= 23$

$\implies x = \frac{23}{99} \: ---(3)$

$ii) Let \:y= 0.\overline{22}$

$\implies y = 0.222222.\cdot\cdot\cdot\:--(4)$

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

$\implies 100x = 22.2222.\cdot\cdot\cdot\:--(5)$

/* Subtract equation (14) From equation (5) , we get*/

$\implies 99x= 22$

$\implies x = \frac{22}{99} \: ---(6)$

$Now, 0.\overline{23} + 0.\overline{22} \\= x + y \\= \frac{23}{99} + \frac{22}{99}\\= \frac{23+22}{99} \\= \frac{45}{99} \\= \frac{5}{11}$

Therefore.,

$\red {0.\overline{23} + 0.\overline{22}}\green {= \frac{5}{11}}$

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