Sequence And Series Question 609
Question: 0.14189189189?. can be expressed as a rational number
[AMU 2000]
Options:
A) $ \frac{7}{3700} $
B) $ \frac{7}{50} $
C) $ \frac{525}{111} $
D) $ \frac{21}{148} $
Show Answer
Answer:
Correct Answer: D
Solution:
0.14189189189…. $ =0.14+0.00189+0.00000189+……. $ $ =\frac{14}{100}+189[ \frac{1}{10^{5}}+\frac{1}{10^{8}}+….\infty ] $ $ =\frac{7}{50}+189,[ \frac{1/10^{5}}{1-(1/10^{3})} ] $ $ =\frac{7}{50}+189,[ \frac{1}{10^{5}}\times \frac{10^{3}}{999} ] $ $ =\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} $ .
BETA
