Question

Express the following in the form
$\frac{p}{q}$
i) 1.419 where 19 are repeating
ii) 18.48 where 48 is repeating

Answer 1

Heya !!!



(1) 1.419 ( bar on 19)


Let X = 1.419


Then X = 1.41919-------(1)


Multiple equation (1) by 10 we get,

10X = 14.1919 --------(2)



Again multiple equation (2) by 100 we get,


1000X = 1419.1919 -----(3)



Subtract equation (2) from equation (3)


1000X = 1419.1919
10X = 14.1919
-------------------------

990X = 1405


X = 1405/990 = 281/198 [ P/Q form ]



Hence,

1.419 ( bar on 19) is of the form of 281/198 which is in the form of P/Q.



(2) 18.48 ( bar on 48)


Let X = 18.48



Then X = 18.4848 ------(1)


Multiple equation (1) by 100 we get,


100X = 1848.4848 -------(2)


subtract equation (1) from equation (2)


100X = 1848.4848
X = 18.4848
--------------------------

99X = 1830

X = 1830/99 = 610/33 [ P/Q form ]


Hence,


18.48 ( bar on 48 ) is of the form of 610/33 which is in the form of P/Q.



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