What is the precision of numbers in Blender? I am using Python scripting to adjust textures on a model, and need to define my own scaling algorithm. What precision?
If I put 0.0000000005 in the UI it ends up to 0.0, see animated GIF below.
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32-bit Floating point representation offers approximately 7.2 decimal digits of precision (7.2 = 7 + 1/5), https://en.wikipedia.org/wiki/Floating_point
Blender limits that to 7 digits. Absolutely safe is to have your number's fraction and integral parts not exceeding 7 digits in total.
If your numbers exceed these limits, the rounding error may be seen, for example, if you set scale X for the default cube to 123456789, it will turn to 123456792.
There is no good way to observe floating point values in the UI, maybe you can print them with Python, as that will avoid Blender's UI conversions.
You can experiment with floating point rounding effects using my online C++ test http://cpp.sh/9pv2l