Rounding errors are caused by the fact that virtually every number in a numerical calculation must be rounded or trimmed to a certain number of digits.
Truncationerrors, on the other hand, occur when an infinite process is replaced by a finite one. This is because computers use a fixed number of bits and, therefore, a fixed number of binary digits to represent numbers. As a result, rounding errors are introduced at each stage of the calculation.
Although an individual rounding error due to a given number in a given numerical step may be small, the cumulative effect can be significant.