To begin with, the decimal representation of real numbers is not unique. To see this consider
a=0.99999...I claim that
a=1To see this note that
10a = 9.99999... a = 0.99999... (subtract) ---------------- 9a = 9 ==> a = 1
In general, there are real numbers that can be expressed either as a number ending in an infinite string of nines or an infinite string of zeros. That's the only way the real representations are not unique! (Proving this is a good exercise ). To obtain a unique decimal representation of a real number we usually impose the convention that it not end in an infinite string of nines.
Fine print, your comments, more links, Peter Alfeld, PA1UM