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.

 Solution:

Assume that

 x = 0.9999…..Eq (1)

Multiplying both sides by 10,

10x = 9.9999…. Eq. (2)

Eq.(2) – Eq.(1), we get

10x = 9.9999…

-x = -0.9999…

___________

9x = 9

x = 1

The difference between 1 and 0.999999 is 0.000001 which is negligible.

Hence, we can conclude that, 0.999 is too much near 1, therefore, 1 as the answer can be justified.