Question

Find the value of 0.123 bar (with steps)

Answer 1

let 0.123 bar be x

then1000x=123.123123123......

if we subtract both..

1000x-x=123.123123....-0.123123123...

999x=123

x=123/999

Answer 2

Let x = $0.\bar{123}$. ------: ( 1 )


As there are 3 digits under bar, multiply by 1000 on both sides,


1000 × x = 1000 × 0.$\bar{123}$

1000x = 123.$\bar{123}$


Now, subtract x from both sides,


1000x = 123.$\bar{123}$
- x = - 0.$\bar{123}$
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999x = 123 { bar cancel }
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x = 123 / 999

x = 41 / 333



From ( 1 ), x = 0.$\bar{123}$


0.$\bar{123} =\dfrac{41}{333}$