Express 0.99999… in the form \(\frac{p}{q} \) . Are you surprised by your answer?
With your teacher and classmates discuss why the answer makes sense.

Let,
x = 0.9999.... (i)


multiplying by eq. (i) by 10 , we get,

10 x = 9.9999......(ii)

On subtracting Eq. (ii) from Eq. (i), we get

(10 x – x) = (9.99999…) – (0.99999…)
\(\Rightarrow \) 9x = 9
\(\Rightarrow \) x = 1

Yes I m surprised
0.9999999..... = 1 because it is extremely closed by 1