Question

Express 1.4191919... in the form p , where p and q are integers and q is not equal to zero.

Answer 1

Solution :

Let x = 1.4191919...---(1)

multiply (1) by 10 , we get

10x = 14.1919.....-----(2)

multiply (2) by 100 ,we get

1000x = 1419.1919....----(3)

Subtract ( 2) from ( 3 ), we

get

990x = 1404

=> x = 1404/990

=> x =(2×9×78)/(2×9×55)

=> x = 78/55 [ p/q form ]

Therefore ,

x = 1.4191919....= 78/55

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