Truncation

 ( Numerical Analysis ) 

In mathematics and computer science, truncation is limiting the number of numerical digit right of the decimal point.

---

Truncation and floor function Truncation of positive real numbers can be done using the floor function. Given a number $x\; \backslash in\; \backslash mathbb\{R\}\_+$ to be truncated and $n\; \backslash in\; \backslash mathbb\{N\}\_0$, the number of elements to be kept behind the decimal point, the truncated value of x is

$\backslash operatorname\{trunc\}(x,n)\; =\; \backslash frac\{\backslash lfloor\; 10^n\; \backslash cdot\; x\; \backslash rfloor\}\{10^n\}.$

However, for negative numbers truncation does not round in the same direction as the floor function: truncation always rounds toward zero, the $\backslash operatorname\{floor\}$ function rounds towards negative infinity. For a given number $x\; \backslash in\; \backslash mathbb\{R\}\_-$, the function $\backslash operatorname\{ceil\}$ is used instead

$\backslash operatorname\{trunc\}(x,n)\; =\; \backslash frac\{\backslash lceil\; 10^n\; \backslash cdot\; x\; \backslash rceil\}\{10^n\}$.

---

Causes of truncation With computers, truncation can occur when a decimal number is type conversion as an integer; it is truncated to zero decimal digits because integers cannot store non-integer real numbers.

---

In algebra An analogue of truncation can be applied to . 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.

Michael Spivak (2025). 9780914098911, Publish or Perish. . ISBN 9780914098911

---

See also

• Arithmetic precision
• Quantization (signal processing)
• Precision (computer science)
• Truncation (statistics)

---

External links

• Wall paper applet that visualizes errors due to finite precision

Post Comment