The transformation is already done in double precision, as is the output of the computed value (controlled by the 'min_sigdigits' param). Is there some particular reason you're asking?
One can see that the numbers begin to deviate in ~ the 7th significant digit.
Here are the lintran parameters:
PACKAGE = lists
TASK = lintran
files = dr1coordstrana
(xfield = 1) field containing x coordinate
(yfield = 2) field containing y coordinate
(min_sig= 15) minimum significant digits to be output
(x1 = 0.) current x origin
(y1 = 0.) current y origin
(xscale = 1.0000000000000E-5) scale factor relative to current origin
(yscale = 1.0000000000000E-5) scale factor relative to current origin
(angle = 0.) rotation angle
(x2 = 0.) new x origin
(y2 = 0.) new y origin
(radians= no) angle in radians?
(mode = ql)
The transformation was being done using double precision values, however the parameter structure was using single precision thereby forcing the calculations to show the round-off. I've changed this for the next update, to patch your v2.14 system I could send you the code change and instructions for relinking the system, otherwise there's no way to change the task at runtime.
An alternative if all you use this task for is to scale those lists is to do it in the CL which is double-precision anyway, e.g.
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