`0.1bar(23)` का मान एक साधारण भिन्न के रूप में निकालिये।

Explanation

`0.123=0.1232323`
`=*1+*0.23+*00023+*0000023+....`
`=(1)/(10)+(23)/(1000)+(23)/(100000)+(23)/(10000000)+.... `
`=(1)/(10)+(23)/(10^(3))+(23)/(10^(5))+(23)/(10^(7))+ ....`
`=(1)/(10)+(23)/(10^(3)){1+(1)/(10^(2))+(1)/(10^(4))+....}`
`=(1)/(10)+(23)/(10^(3)){(1)/(1-(1)/(10^(2)))}`
`=(1)/(10)+(23)/(10^(3))xx(10^(2))/(10^(2)-1)`
`=(1)/(10)+(23)/(10)xx(1)/(99)`
`=(1)/(10)+(23)/(990)`
`=(122)/(990)=(61)/(495)`