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# 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