Rounding errors
A rounding error or a rounding difference is the deviation of a rounded number from the original. Rounding saves effort at the expense of accuracy. Rules for rounding can be found, for example, in the DIN 1333 and IEEE 754 standards .
Rounding errors occur when
- not all decimal places are taken into account for a calculation , for example the infinite number of digits of the circle number , or
-
by an invoice more points arise when
- are representable or
- are significant ( sham accuracy ).
Rounding errors are not errors in the strict sense because they are intended. They are to be distinguished from errors in rounding, for example instead of .
If several invoices are carried out one after the other with rounded numbers, the rounding errors can increase with each invoice. If several rounded numbers are included in an invoice, the error propagation must be taken into account.
In computer rounding errors occur when using floating point on. They result from the only finite representation of the same. For example, in recursive digital filters (see also digital filter ), so-called limit cycles can occur, in which the output of the filter - even if the input signal has long since decayed - represents a periodic sequence that usually has a low power .
