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A comment on 0.30000000000000004. Parent comment
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.
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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.