Roundoff errors arise because digital computers cannot represent some quantities exactly. They are
important to engineering and scientific problem solving because they can lead to erroneous results. In certain
cases, they can actually lead to a calculation going unstable and yielding obviously erroneous results. Such
calculations are said to be ill-conditioned. Worse still, they can lead to subtler discrepancies that are difficult to
detect.
There are two major facets of roundoff errors involved in numerical calculations:
1. Digital computers have magnitude and precision limits on their ability to represent numbers.