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January 22nd, 2019, 04:31 PM   #41
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Originally Posted by zylo View Post
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:

Decimals and the Continuum
Yeah, I think everyone knows that craftsmen and engineers use approximations that suit the tolerances they work too. It has nothing whatever to do with the construction of the real numbers.
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January 22nd, 2019, 08:36 PM   #42
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Originally Posted by zylo View Post
. . . by standard (High School) division.
Using division isn't an explanation of how to put a period after a natural number and then read it in reverse to get the decimal for 1/9. Is that your best effort?
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