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Q. The value of $0.0373737 $..... is

COMEDKCOMEDK 2008Probability - Part 2

Solution:

Let $x = 0.0\bar{37} \Rightarrow 10x = 0.\bar{37}$
$ \Rightarrow 1000x = 37.\bar{37} = 37 + 0.\bar{37} = 37 + 10 x$
$\Rightarrow 990 x = 37 \Rightarrow x = \frac{37}{990}$