The mantissa of a FLOAT is a 53-bit binary fraction, and it can exactly represent only rational numbers whose denominator is a power of 2. This means that 0.1 can't be represented exactly, the value stored is actually closer to 0.1000000000000000055511. Neither can 0.9 or 0.005. Any integer value under 15 digits long can be stored exactly, as can binary fractions like 0.5, 0.25, 0.125, etc.

Floating-point calculations are done in the CPU with 80-bit precision and the result is rounded to 53 bits, which in many cases works very well and the approximation errors cancel out. 10 x 0.1 results in exactly 1.0, for example. But repeatedly adding 0.1 means the same tiny error is added at each step and it eventually becomes noticable as shown in the examples posted above.