Decimal floating point (3 or 4 binary bits), and the rest of the significand uses the densely packed decimal (DPD) encoding. Unlike the binary integer significand version, where the exponent changed position and came before the significand, this encoding combines the leading 2 bits of the exponent and the leading digit (3 or 4 bits) of the significand into the five bits that follow the sign bit. This is followed by a fixed-offset exponent continuation field. Finally, the significand continuation field made of 2, 5, or 11 10-bit "declets", each encoding 3 decimal digits. If the first two bits after the sign bit
Decimal representation for some "n". By formula_38, "x" will end in zeros. Some real numbers have decimal expansions that eventually get into loops, endlessly repeating a sequence of one or more digits: Every time this happens the number is still a rational number (i.e. can alternatively be represented as a ratio of an integer and a positive integer). Also the converse is true: The decimal expansion of a rational number is either finite, or endlessly repeating. Decimal representation A decimal representation of a non-negative real number "r" is an expression in the form of a series, traditionally written as a sum where