MCQ
$0.14189189189….$ can be expressed as a rational number
- A$\frac{7}{{3700}}$
- B$\frac{7}{{50}}$
- C$\frac{{525}}{{111}}$
- ✓$\frac{{21}}{{148}}$
$ = 0.14 + 0.00189 + 0.00000189 + .......$
$ = \frac{{14}}{{100}} + 189\left[ {\frac{1}{{{{10}^5}}} + \frac{1}{{{{10}^8}}} + ....\infty } \right]$
$ = \frac{7}{{50}} + 189\,\left[ {\frac{{1/{{10}^5}}}{{1 - (1/{{10}^3})}}} \right]$$ = \frac{7}{{50}} + 189\,\left[ {\frac{1}{{{{10}^5}}} \times \frac{{{{10}^3}}}{{999}}} \right]$
$ = \frac{7}{{50}} + \frac{{189}}{{999 \times 100}}$
$ = \frac{7}{{50}} + \frac{7}{{3700}} = \frac{7}{{50}} + \frac{7}{{25 \times 148}}$$ = \frac{{21}}{{148}}$.
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