Question

the value of 2.423 bar over 23​

Answer 1

$Let \: x = 2.4\overline{23}$

$\implies x = 2.4232323\cdot\cdot\cdot \: --(1)$

/* Multiplying bothsides by 10 ,we get */

$\implies 10x = 24.232323\cdot\cdot\cdot \: --(2)$

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

$\implies 1000x = 2423.2323\cdot\cdot\cdot \: --(3)$

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

$\implies 1000x - 10x = 2423.2323\cdot\cdot\cdot - 24.232323\cdot\cdot\cdot$

$\implies 990x = 2399$

$\implies x = \frac{2399}{990}$

Therefore.,

$\red{ 2.4\overline{23}} \green {= \frac{2399}{990}}$

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