Express 0.99999 .... in the form `p/q`. . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Answer

N/a

Explanation

Let `x=0.999999 . . .=0.bar(9)` . . .(1)
Multiple both sides by 10, we get `(because` one digit is repeating)
`10x=9.9999. . .` . . .(2)
subtracting equation (1) from (2), we get
`{:(10x=9.9999 . . .),(ul(_x=_-0.9999. . .)),(9x=9):}`
`rArr" "x=(9)/(9)=1`
`rArr" "0.99999 . . .=1`.
Explanation : As 0.99999 . . . gose forever. It means is no gap between 0.99999 . . . and 1.
Gence, both are equal.