See also: http://cs.furman.edu/digitaldomain/more/ch6/dec_frac_to_bin.htm http://cs.furman.edu/digitaldomain/more/ch6/dec_frac_to_bin.... ".1 (decimal) = .000

See also: http://cs.furman.edu/digitaldomain/more/ch6/dec_frac_to_bin.htm http://cs.furman.edu/digitaldomain/more/ch6/dec_frac_to_bin.... ".1 (decimal) = .00011001100110011 . . . (base 2)" Notice the repeating pattern? The exact number must have infinite number of binary digits. Wherever you cut (whichever fixed number of bits you want to keep) you lose something.