Sequence And Series Question 627
Question: $ 0.5737373……= $
[Karnataka CET 2004]
Options:
A) $ \frac{284}{497} $
B) $ \frac{284}{495} $
C) $ \frac{568}{990} $
D) $ \frac{567}{990} $
Show Answer
Answer:
Correct Answer: C
Solution:
Given series 0.5737373?? = 0.5 + 0.073 + 0.00073 = 0.5 + $ \frac{73}{1000}+\frac{73}{100000}+…. $ = $ 0.5+73[ \frac{1}{1000}+\frac{1}{100000}+….. ] $ = $ 0.5+73[ \frac{1/1000}{1-\frac{1}{100}} ] $ = $ 0.5+\frac{73}{1000}.\frac{100}{99}=\frac{5}{10}+\frac{73}{990} $ = $ \frac{495+73}{990}=\frac{568}{990} $ .
BETA
