The message 0.538 in the previous example could have been encoded by the equally short fractions 0.534, 0.535, 0.536, 0.537 or 0.539. This suggests that the use of decimal instead of binary introduced some inefficiency. This is correct; the information content of a three-digit decimal is formula_1 bits; the same message could have been encoded in the binary fraction 0.10001010 (equivalent to 0.5390625 decimal) at a cost of only 8 bits. (The final zero must be specified in the binary fraction, or else the message would be ambiguous without external information such as compressed stream size.)