Round-off error

Definition

Round-off error occurs when a floating-point number cannot be represented exactly in binary form, resulting in a small discrepancy. This often affects calculations involving decimal numbers.

5 Must Know Facts For Your Next Test

1. Round-off errors are inherent in floating-point arithmetic due to the finite precision of binary representation.
2. These errors can accumulate and significantly affect the outcome of iterative calculations or complex expressions.
3. Python's built-in float type adheres to IEEE 754 standards for double-precision floating-point numbers, which is susceptible to round-off error.
4. Using rounding functions like round() can help mitigate but not completely eliminate round-off errors in Python.
5. Understanding and managing round-off errors is crucial for accurate numerical computations in programming.

Review Questions

• What causes round-off errors in floating-point arithmetic?
• How does Python handle floating-point numbers and what standard does it follow?
• What are some methods to manage or reduce the impact of round-off errors in Python?

Related terms

Floating-Point Arithmetic: A method of representing real numbers that supports a wide range of values by using a fractional component (mantissa) and an exponent.

IEEE 754:

A technical standard for floating-point computation established by the Institute of Electrical and Electronics Engineers, widely used in computer systems.

Precision:

The degree to which the exactness of a number is expressed within its representation; higher precision means more digits are used to represent the number.