Editing Round-off error (section)

=== Multiplication ===

In general, the product of two p-digit significands contains up to 2p digits, so the result might not fit in the significand.<ref name="Forrester_2018"/> Thus roundoff error will be involved in the result.

* For example, consider a normalized floating-point number system with the base <math>\beta=10</math> and the significand digits are at most <math>2</math>. Then <math>fl(77) = 7.7 \times 10^{1}</math> and <math>fl(88) = 8.8 \times 10^{1}</math>. Note that <math>77 \times 88=6776</math> but <math>fl(6776) = 6.7 \times 10^{3}</math> since there at most <math>2</math> significand digits. The roundoff error would be <math>6776 - fl(6776)  = 6776 - 6.7 \times 10^{3}=76</math>.