Why can't decimal numbers be represented exactly in binary?

Question

There have been several questions posted to SO about floating-point representation. For example, the decimal number 0.1 doesn\'t have an exact binary representation, so it\'

Answer 1

you know integer numbers right? each bit represent 2^n

2^4=16
2^3=8
2^2=4
2^1=2
2^0=1

well its the same for floating point(with some distinctions) but the bits represent 2^-n 2^-1=1/2=0.5
2^-2=1/(2*2)=0.25
2^-3=0.125
2^-4=0.0625

Floating point binary representation:

sign  Exponent    Fraction(i think invisible 1 is appended to the fraction )
B11  B10 B9 B8   B7 B6 B5 B4 B3 B2 B1 B0