Editing Floating-point arithmetic (section)

=== Multiplication and division ===
To multiply, the significands are multiplied while the exponents are added, and the result is rounded and normalized.

   e=3;  s=4.734612
 × e=5;  s=5.417242
 -----------------------
   e=8;  s=25.648538980104 (true product)
   e=8;  s=25.64854        (after rounding)
   e=9;  s=2.564854        (after normalization)

Similarly, division is accomplished by subtracting the divisor's exponent from the dividend's exponent, and dividing the dividend's significand by the divisor's significand.

There are no cancellation or absorption problems with multiplication or division, though small errors may accumulate as operations are performed in succession.<ref name="Goldberg_1991"/> In practice, the way these operations are carried out in digital logic can be quite complex (see [[Booth's multiplication algorithm]] and [[Division algorithm]]).<ref group="nb" name="NB_2"/>