Q. 84.0( 56 Votes )

Express each of t

Answer :

(i). 0.5 = 5/10

Simplifying it in the same p/q form,


0.5 = 1/2


It cannot be further simplified in p/q form.


1/2 is in the form p/q, where p = 1 and q = 2 are integers and q = 2 ≠ 0.


Hence, the answer is 1/2.


(ii).


This has to be converted in p/q form.


Let ,


That is, x = 3.88888… …(i)


Multiply 10 on both sides,


10 × x = 10 × 3.88888…


10x = 38.8888… …(ii)


Subtracting equations (i) from (ii), we get


10x – x = 38.8888… - 3.88888…


9x = 35


x = 35/9


35/9 is in the form of p/q, where p = 35 and q = 9 are integers and q = 9 ≠ 0.


Thus, .


(iii).


This has to be converted in p/q form.


Let ,


That is, x = 0.363636… …(i)


Multiply 100 on both sides,


100 × x = 100 × 0.363636…


100x = 36.363636… …(ii)


Subtracting equations (i) from (ii), we get


100x – x = 36.363636… - 0.363636…


99x = 36


x = 99/36


Simplifying it further,


x = 11/4


11/4 is in the form of p/q, where p = 11 and q = 4 are integers and q = 4 ≠ 0.


Thus, .


(iv).


This has to be converted in p/q form.


Let ,


That is, x = 3.127777… …(i)


Multiply 100 by equation (i),


100 × x = 100 × 3.127777…


100x = 312.7777… …(ii)


Multiply 1000 by equation (ii),


1000 × x = 1000 × 3.127777…


1000x = 3127.7777… …(iii)


Subtract equation (ii) from (iii), we get


1000x – 100x = 3127.7777… - 312.7777…


900x = 2815


x = 2815/900


x = 563/180


563/180 is in the form of p/q, where p = 563 and q = 180 are integers and q = 180 ≠ 0.


Thus, .


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