Decimal numbers that may be expressed as a fraction, the denominator of which is a power of ten. For example, the numerals formula_5 represent the fractions , , . More generally, a decimal with digits after the separator represents the fraction with denominator , whose numerator is the integer obtained by removing the separator. Expressed as a fully reduced fraction, the decimal numbers are those, whose denominator is a product of a power of 2 by a power of 5. Thus the smallest denominators of decimal numbers are The "integer part", or "integral part" of a decimal is the integer written
Densely packed decimal is a refinement of Chen–Ho encoding; it gives the same compression and speed advantages, but the particular arrangement of bits used confers additional advantages: In 1971, Tien Chi Chen and Irving Tze Ho devised a lossless prefix code (known as Chen–Ho encoding since 2000) which packed three decimal digits into ten binary bits using a scheme which allowed compression from or expansion to BCD with only two or three gate delays in hardware. Densely packed decimal is a refinement of this, devised by Mike F. Cowlishaw in 2002, which was incorporated into the IEEE 754-2008 and standards for decimal floating-point.