Floating point arithmetic is different from regular arithmetic

1. Equal or not equal

0.1 + 0.2:
0.3000000000000000444089209850062616169452667236328125
0.3:
0.299999999999999988897769753748434595763683319091796875

0.1 + 0.3:
0.40000000000000002220446049250313080847263336181640625
0.4:
0.40000000000000002220446049250313080847263336181640625

2. The addition is not associative and distributive (in general), but it is commutative.

a fp(+) b = b fp(+) a
(a fp(+) b) fp(+) c ≠ a fp(+) (b fp(+) c)

3. Floating point numbers are not distributed uniformly on the real axis.

Challenge problem: can you calculate the exact value of $\sin \pi$ on a computer?

Floating point numbers, Floating point arithmetic and unit roundoff error