Tach to arfa brane;3138834... Let's try a simple exercise. Start with 0.n 1. Multiply be [tex said:10^{-1}[/tex]. You get 0.0n, right? In what direction from the decimal point did zero propagate? (hint: you were taught the answer in 5-th grade)

2. Multiply again by $$10^{-1}$$. You get 0.00n, right? In what direction from the decimal point did zero propagate?

You miss the point that the decimal notation per se is represented as 00000.000000 to imply infinite PLACES extending in both directions from the transition zone where the DECIMAL POINT is included in the notation of the system PER SE.

However, when we actually USE the decimal system notation for ACTUAL STRINGS, then the infinity of zeros is NOT continuous because the actual significant digits OCCUPYING any one or more of those places ALWAYS INTERRUPTS the infinity-of-zeros continuity of the notation per se.

Hence the extension of zeros to infinity from the decimal point (for a FRACTIONAL string) is always interrupted by the 9 in .9 (9/10ths), and by the .09 (9/100ths) etc, no matter how many times you divide by ten.

Furthermore, in that FRACTIONAL string, the only effect on the 'value' of the fractional string (to change it from 9/10ths to 9/100ths) is brought by the LEADING ZEROS introduced into the string FROM the decimal point BUT in front of the 9 (or whatever string of significant digits involved in the FRACTIONAL value).

And once you see that LEADING zeros are important to the actual value of a fractional string, then the leading zeros extends to infinity UNINTERRUPTED and TO THE LEFT of the fractional string, and hence the zeros to the left extend past the decimal point notation symbol and CONTINUE UNINTERRUPTED to infinity to the LEFT of the decimal point (just as arfa brane is explaining to you, again).

Ok?