A) \[\frac{7}{3700}\]
B) \[\frac{7}{50}\]
C) \[\frac{525}{111}\]
D) \[\frac{21}{148}\]
Correct Answer: D
Solution :
0.14189189189.... \[=0.14+0.00189+0.00000189+.......\] \[=\frac{14}{100}+189\left[ \frac{1}{{{10}^{5}}}+\frac{1}{{{10}^{8}}}+....\infty \right]\] \[=\frac{7}{50}+189\,\left[ \frac{1/{{10}^{5}}}{1-(1/{{10}^{3}})} \right]\]\[=\frac{7}{50}+189\,\left[ \frac{1}{{{10}^{5}}}\times \frac{{{10}^{3}}}{999} \right]\] \[=\frac{7}{50}+\frac{189}{999\times 100}\] \[=\frac{7}{50}+\frac{7}{3700}=\frac{7}{50}+\frac{7}{25\times 148}\]\[=\frac{21}{148}\].
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