27 bits Are Not Enough for 8-digit Accuracy From the inequality 10^8 < 2^27, we are likely to conclude that we can represent 8-digit decimal floating-point numbers accurately by 27-bit floating-point numbers. However, we need 28 significant bits to represent some 8-digit numbers accurately. In general, we can show that if 10^p < 2^q-1, then q significant bits are always enough for p-digit decimal accuracy. Finally, we can define a compact 27-bit floating-point representation that will give 28 significant bits, for numbers of practical importance. CACM February, 1967 Goldberg, I. B. CA670208 JB February 28, 1978 2:38 PM 1634 5 1634 1634 5 1634 1634 5 1634 1783 5 1634 1843 5 1634 1634 6 1634 1634 6 1634 1783 6 1634