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