The value of overline{0.037},where overline{0 | vedclass

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(D) Let $x = 0.037037037...$ This is a geometric series with the first term $a = \frac{37}{1000}$ and common ratio $r = \frac{1}{1000}$. The sum of an

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$\frac{37}{999}$

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(D) Let $x = 0.037037037...$ This is a geometric series with the first term $a = \frac{37}{1000}$ and common ratio $r = \frac{1}{1000}$. The sum of an infinite geometric series is given by $S = \frac{a}{1-r}$. Substituting the values: $S = \frac{37/1000}{1 - 1/1000} = \frac{37/1000}{999/1000} = \frac{37}{999}$. Simplifying the fraction: $\frac{37}{999} = \frac{1}{27}$. Since both options $B$ and $D$ are mathematically equivalent,and $\frac{37}{999}$ is the direct representation of the repeating decimal,the correct choice is $D$ (or $B$ as they are equal).

The value of $\overline{0.037}$,where $\overline{0.037}$ stands for the number $0.037037037...$,is

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