A simple question on distributive property of floating-point arithmetic

Questions
,
1

Please comment on the following:

a = 11.56;
100000 (1 + a/100) // Floor
1000 (100 + a) // Floor
a =.;

I guess it’s a result of numerical computations and settings for accuracy, precision, etc., but nevertheless …

2

Floating-point arithmetic addition and multiplication (in general, not just in Mathematica) are commutative but need not be associative or distributive.