I didn't ask for the decimal representation of 1/9, zylo. I asked how you get it by using your definition. You've shown how some other numbers are produced, but not 1/9.

What is 1/9?

1/9 is the infinite (unending) decimal .111......., by standard (High School) division. This is an example of how one arrives at decimal representation.

What is the infinite (unending) decimal .111.....?

An infinite decimal whose sum evaluated to n places gets arbitrarily close to 1/9 as n increases indefinitely. The comparison can be made because .1111 .. . evaluated to n places is a rational number.

What is 1/9 in radix 9 notation? .1: Divide a unit line into nine intervals. 1/9 is end of first interval.

That's the way a ruler works:

Divide the standard inch in half: 1/2

Divide each interval in half: 1/4

Divide each interval in half again: 1/8

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A carpenter doesn't deal in decimals. His ruler (a tape) is divided in 1/32's. He works to 1/32's or maybe 1/16's.

A cabinet maker would work to 1/64th's. His ruler is probably a yard stick graduated to 1/64th's.

A machinist deals in thousandths. His ruler is a micrometer or vernier caliper which reads to three (.001) or four (.0001) decimal places.

There is constant conversion in practice: 1/16 = .0625 for example

To convert Pi to a decimal representation: Take a circle of diameter 1. Then unwind the circle onto a line with same unit 1. The decimal representation of the point where the line ends can be found as in:

http://mymathforum.com/real-analysis/345652-decimals-continuum.html