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 unique. The number defined by a decimal representation is often written more briefly as That is to say, "a" is the integer part of "r", not necessarily between 0 and 9, and "a", "a", "a", ... are the digits forming the fractional part of "r". Both notations above are, by definition, the following limit of a sequence: Any real number can be approximated to any desired degree of accuracy by rational numbers with finite decimal representations. Assume formula_4. Then for every integer formula_5 there is a finite decimal formula_6 such that Proof: Let formula_8, where formula_9. Then formula_10, and the