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Mathematics

Find (using G.P.) the value of $0.4\overline{23}$ .

AP GP

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Answer

Let, x = $0.4\overline{23}$ .

⇒ x = 0.4232323……

⇒ 10x = 4.232323…….

⇒ 1000x = 423.2323…….

⇒ 1000x - 10x = 423.2323……. - 4.232323…….

⇒ 990x = 419

⇒ x = $\dfrac{419}{990}$

Hence, $0.4\bar{23} = \dfrac{419}{990}$ .

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