Convert $0.42 ¯ ¯¯¯¯¯¯ ¯ 213$ into a fraction.

\frac{4317}{9990}

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\frac{4317}{9999}

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\frac{4316}{9000}

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None of these

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Solution

The correct option is B $\frac{4317}{9990}$
$10 x = 0.42 ¯ ¯¯¯¯¯¯ ¯ 213$
$100 x = 42. ¯ ¯¯¯¯¯¯ ¯ 213$ $. . . .1$
$100000 x = 42213. ¯ ¯¯¯¯¯¯ ¯ 213$ $. . . .2$
Subtract $(1)$ from $(2)$
$99900 x = 42171$

$x = \frac{42171}{99900}$

So, option $A$ is correct.

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