Question

Find the value of 19.999... in the form p/q, where p and q are integers and q not equal to 0

Answer 1

Let x = 19.99999......
So, 10x= 199.9999....
    9x = 199.999.... - 19.999999
     x = 180/9
     x = 20
Answer is surprising but correct as nothing can be added to 19.99.... to make it 20. And there are no rationals between them.

Answer 2

hello,
let 19.999.....= x           .................1
multiply 1 by 10
199.999........=10x          ................2
subtract 1 from 2
199.999......-19.999.....=10x-x
180=9x
x=20
(although it is not possible but we have to take it in the form of p/q)
here,p=20
q=1
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