Truncation

Truncation is the process of limiting the number of digits right of the decimal point by discarding the least significant digits. It is a common operation in computer science, mathematics, and statistics.

Mathematics

In mathematics, truncation is used to approximate a real number by removing its fractional part. For example, truncating the number 3.14159 to two decimal places results in 3.14. This is different from rounding, where the number is approximated to the nearest value based on the digits being discarded.

Computer Science

In computer science, truncation is often used in floating-point arithmetic to manage precision and storage. Truncation can lead to truncation error, which is the difference between the actual number and the truncated number. This error is significant in fields requiring high precision, such as scientific computing and cryptography.

Statistics

In statistics, truncation can occur in data collection when values below or above a certain threshold are excluded. This is different from censoring, where values are only partially known. Truncated data can lead to biased estimates and requires special statistical techniques to analyze.

Applications

Truncation is used in various applications, including:

• Numerical analysis: To simplify calculations and reduce computational load.
• Signal processing: To limit the bandwidth of a signal by discarding high-frequency components.
• Data compression: To reduce the size of data by removing less significant parts.

Related Concepts

• Rounding
• Floating-point arithmetic
• Truncation error
• Censoring (statistics)
• Numerical analysis

See Also

• Approximation
• Precision (computer science)
• Significant figures
• Data truncation