The correct expression of 6.overline{46} in t | vedclass

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Question

(D) Let $x = 6.\overline{46}$.This can be written as $x = 6.464646...$Multiply by $100$ to shift the decimal point: $100x = 646.464646...$Subtract the

Vedclass · Accepted Answer

$\frac{640}{99}$

Vedclass · Answer

(D) Let $x = 6.\overline{46}$.This can be written as $x = 6.464646...$Multiply by $100$ to shift the decimal point: $100x = 646.464646...$Subtract the original equation $x = 6.464646...$ from $100x = 646.464646...$:$100x - x = 646.464646... - 6.464646...$$99x = 640$$x = \frac{640}{99}$Alternatively,$6.\overline{46} = 6 + 0.\overline{46} = 6 + \frac{46}{99} = \frac{6 	imes 99 + 46}{99} = \frac{594 + 46}{99} = \frac{640}{99}$.

The correct expression of $6.\overline{46}$ in the fractional form is

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