MCQ
The value of $\overline {0.037} $ where,  $\overline {.037} $ stands for the number $0.037037037........$ is
  • A
    $\frac{{37}}{{1000}}$
  • B
    $\frac{1}{{27}}$
  • C
    $\frac{1}{{37}}$
  • $\frac{{37}}{{999}}$

Answer

Correct option: D.
$\frac{{37}}{{999}}$
d
(d) Given series $0.037037037……$

$= 0.037+0.000037+0.0000000037+…….$

= $\frac{{37}}{{{{10}^3}}} + \frac{{37}}{{{{10}^6}}} + \frac{{37}}{{{{10}^9}}} + ......$

= $37\left[ {\frac{1}{{{{10}^3}}} + \frac{1}{{{{10}^6}}} + \frac{1}{{{{10}^9}}} + ....} \right]$

= $37\left[ {\frac{{1/{{10}^3}}}{{1 - 1/{{10}^3}}}} \right] $

$= 37\left[ {\frac{1}{{{{10}^3}}}.\frac{{{{10}^3}}}{{999}}} \right]$ = $\frac{{37}}{{999}}$.

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