Question

Show that 0,235353535..... can be expressed in the form p/q ,where and are integers and q not equal zero

Answer 1

Heya !!!





0.235 ( bar on 35)





Let X = 0.235



Then X = 0.2353535 ----------(1)




Multiply equation (1) by 10 we get,




10X = 2.353535 ------------(2)




Again multiply equation (2) by 100 we get,





1000X = 235.353535 ----------(3)




Subtract equation (2) from equation (3) we get,





1000X = 235.353535

10X = 2.353535

------------------------------



990X = 233 [ Bar cancelled ]





X = 233/990





Hence,



0.235 ( bar on 35) is in the form of 233/990 which is in the form of P/Q.



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