What is a common consequence of finite precision in floating-point arithmetic?

• A. Arithmetic is always exact.
• B. Rounding errors occur.
• C. Numbers cannot be added.
• D. Negative numbers cannot be represented.

Answer: (B)

Finite precision in floating-point representations means only a limited set of values can be stored. Because many real numbers can’t be represented exactly with a fixed number of bits, the results of most arithmetic operations must be rounded to the nearest representable value. This rounding creates small errors that can accumulate over multiple calculations. For example, 0.1 cannot be represented exactly in binary, so summing 0.1 and 0.2 often yields a result that isn’t exactly 0.3. Other statements aren’t true because arithmetic isn’t always exact, numbers can be added, and negative numbers can be represented in floating-point formats.