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 do not allow an exact representation for all real numbers, so e.g. for the real number . Nevertheless, they allow approximating every real number with any desired accuracy, e.g., the decimal 3.14159 approximates the real , being less than 10 off; and so decimals are widely used in science, engineering and everyday life. More precisely, for every real number "x", and every positive integer "n", there are two decimals "l" and "u", with at most "n" digits after the decimal mark, such that "l" ≤ "x" ≤ "u" and ("u" – "l") = 10. Numbers are very often obtained as