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Question

How do we represent 0.123¯¯¯¯¯¯¯¯456 in fraction?


A

41111333000

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B

333399000

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C

41111999000

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D

1233399000

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Solution

The correct option is A

41111333000


Let x=0.123¯¯¯¯¯¯¯¯456

Multiplying the above equation with 1000 and 1000000, we get the following equations:
1000x=123.¯¯¯¯¯¯¯¯456 ........................(1)
1000000x=123456.¯¯¯¯¯¯¯¯456 .....................(2)

On subtracting (1) from (2), we get,
1000000x1000x=123456.¯¯¯¯¯¯¯¯456123.¯¯¯¯¯¯¯¯456
999000x=123333
x=123333999000
x=41111333000


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