MCQ
$0.\mathop {423}\limits^{\,\,\,\, \bullet \,\,\, \bullet \,} = $
- ✓$\frac{{419}}{{990}}$
- B$\frac{{419}}{{999}}$
- C$\frac{{417}}{{990}}$
- D$\frac{{417}}{{999}}$
$ = 0.4 + 0.023 + 0.00023 + 0.0000023 + ........\infty $
$ = \frac{4}{{10}} + \frac{{23}}{{{{10}^3}}} + \frac{{23}}{{{{10}^5}}} + \frac{{23}}{{{{10}^7}}}........\infty $
$ = \frac{4}{{10}} + \frac{{23}}{{{{10}^3}}}\left[ {1 + \frac{1}{{{{10}^2}}} + \frac{1}{{{{10}^4}}} + ..........\infty } \right]$
$ = \frac{4}{{10}} + \frac{{23}}{{1000}}\left( {\frac{1}{{1 - \frac{1}{{{{10}^2}}}}}} \right) = \frac{4}{{10}} + \frac{{23}}{{990}} = \frac{{419}}{{990}}$.
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