Question

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.

Answer 1

Let $x=0.99999\cdots$ ...(1)

Multiply eq (1) by $10$ we get

$10x=9.9999\cdots$ ...(2)

Substract (1) from (2), we get

$\Rightarrow 9x=9$

$\Rightarrow x=\frac{1}{1}=1$

Here,

$p=1$ and $q=1$

Thus,

$0.9999\cdots =1$