Lower and Upper bound proof in R

[MotoPayton]

I am getting lost in the proof in the 5th line when it says there are 10 numbers that have the same kth digit as x. Why 10? I don't understand where this number is coming from and it doesn't seem arbitrary.

the rest of the proof
http://i603.photobucket.com/albums/tt113/KtmPayton/0306132314.jpg

 

[pwsnafu]

From the fact that the decimal expression is in base 10.
Walk through the proof with a specific example.