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in Geometric Progressions by (15.7k points)

Write the value of 0.\(\overline{423}\) in the form of a simple fraction.

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1 Answer

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by (15.2k points)

Let, x = 0.423423423… …(i) 

Multiplying this equation by 1000 on both the sides so that repetitive terms cancel out and we get:

1000x = 423.423423423… …(ii) 

Equation (ii) - (i), 

⇒ 1000x - x = 423.423423423 - 0.423423423 = 423 

⇒ 999x=423

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