When you see the term IEEE standard in this book without a number following, it means IEEE Standard 754. The IEEE standards ensure that computers represent real numbers as accurately as possible and that computers perform arithmetic on real numbers as accurately as possible. Although there are infinitely many real numbers, a computer can represent only a finite number of them.
Computers represent real numbers as binary floating-point numbers .
Other real numbers that can be represented exactly in decimal have repeating digits in binary and hence cannot be represented exactly, as shown in Table 1-1 . Errors of this kind are unavoidable in any computer approximation of real numbers. Because of these errors, sums of fractions are often slightly incorrect. When a numerics environment is performing a floating-point operation, it calculates the result to a predetermined number of binary digits. This number of digits is called the precision.