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.
Solution:
Let $x=0.9999 \ldots$
$10 x=9.9999 \ldots$
$10 x=9+x$
$9 x=9$
$x=1$
Let $x=0.9999 \ldots$
$10 x=9.9999 \ldots$
$10 x=9+x$
$9 x=9$
$x=1$