Question

Express `0.6+0.bar7+0.4bar7` in the form `p/q` where p and q are integers and `q ne 0`.

Answer 1

Let `x=0.bar7= 0.777`
on multiplying both sides of Eq. (i) by 10, we get
10x=7.77…..
on subtrracting Eq. (i) from Eq. (ii) we get
10x-x= (7.77…)-(0.77….)
9x=7
`x=7/9`
now let `y=0.4bar7 =0.4777…..`
on multiplying both sides of Eq. (ii) by 10, we get
10y= 4.777....
on multiplying both sides . Eq . (iv) by 10, we get
100y= 47.777.....
on subtracting Eq. (iv) from (v), we get
(100y-10y)= (47.777....) - (4.777....)
90y = 43 `43/90`
`0.6 + 0.bar7+ 0.4bar7=6/10 + 7/9+43/90`
`(54+70+43)/90=167/90`