Question

Express in the form of p/q
1: 0.328 bar on 328
2: 0.585 bar on 585
3: 15.712 bar 12
4: 0.245 bar on 245

Answer 1

Heya !!!



(1) 0.328 ( bar on 328)


Let X = 0.328


Then X = 0.328328 --------(1)


Multiple equation (1) by 1000 we get,


1000X = 328.328328 -------(2)



Subtract equation (1) from equation (2) we get,


1000X = 328.328328

X = 0.328328
-----------------------------

999X = 328

X = 328/999 [ P/Q from ]



Hence,


0.328 ( bar on 328) is of the form of 328/999 which is in the from of P/Q.





(2) 0.585 ( bar on 585)




Let X = 0.585


Then X = 0.585585 --------(1)



Multiple equation (1) by 1000 we get,


1000X = 585.585585 -------(2)



Subtract equation (1) from equation (2) we get,


1000X = 585.585585

X = 0.585585
-----------------------------

999X = 585 [ Bar cancelled ]


X = 585/999 [ P/Q from ]



Hence,


0.585 ( bar on 585) is of the form of 585/999 which is in the form of P/Q.




(3) 15.712 ( bar on 12)


Let X = 15.712


Then X = 15.71212 ---------(1)


Multiple equation (1) by 10 we get,


10X = 157.1212 -----------(2)



Again multiple equation (2) by 100 we get,


1000X = 15712.1212



Subtract equation (1) from equation (2) we get,


1000X = 15712.1212

10X = 157.1212
--------------------------


990X = 15555


X = 15555/990 = 31111/198 [ P/Q form ]



Hence,

15.712 ( bar on 12) is in the form of 31111/198 which is in the form of P/Q.





(4) Similar to (1) and (2)




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