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Question

Express 0.6+0.7bar+0.47bar in the form of p/q where p and q are integers and q not = 0?

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Solution

Let x = 0.6 .............1Multiplying 1 by 10, we get,10x = 10 × 0.6 10x = 6.6 ............2Now subtracting 1 from 2, we get, 10x - x = 6.6 - 0.6 9x = 6 x = 69 = 23Let y = 0.7 ............3Multiplying 3 by 10 10 × y = 10 × 0.7 10y = 7.7 .............4Subtracting 3 from 4, we get, 10y - y = 7.7 - 0.7 9y = 7 y = 79Let z = 0.47 ............5Multiplying 5 by 100 100 × z = 100 × 0.47 100z = 47.47 ............6Subtracting 5 from 6, we get 100z - z = 47.47 - 0.47 99z = 47 z = 4799Therefore, x + y + z = 0.6 + 0.7 + 0.47 = 23 + 79 + 4799 =66 + 77 + 4799 = 19099

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