For example, consider the real numbers
To truncate these numbers to 4 decimal digits, we only consider the 4 digits to the right of the decimal point.
The result would be:
Truncation and floor function
Truncation of positive real numbers can be done using the floor function. Given a number to be truncated and , the number of elements to be kept behind the decimal point, the truncated value of x is
However, for negative numbers truncation does not round in the same direction as the floor function: truncation always rounds toward zero, the floor function rounds towards negative infinity.
Causes of truncation
With computers, truncation can occur when a decimal number is typecast as an integer; it is truncated to zero decimal digits because integers cannot store real numbers (that are not themselves integers).
An analogue of truncation can be applied to polynomials. In this case, the truncation of a polynomial P to degree n can be defined as the sum of all terms of P of degree n or less. Polynomial truncations arise in the study of Taylor polynomials, for example.
- Arithmetic precision
- Floor function
- Quantization (signal processing)
- Precision (computer science)
- Truncation (statistics)
- Wall paper applet that visualizes errors due to finite precision