How do we represent 0.123¯¯¯¯¯¯¯¯456 in fraction?
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,
1000000x−1000x=123456.¯¯¯¯¯¯¯¯456−123.¯¯¯¯¯¯¯¯456
⇒ 999000x=123333
⇒ x=123333999000
⇒ x=41111333000