Editing Fixed-point arithmetic (section)

===Division===
To divide two fixed-point numbers, one takes the integer quotient of their underlying integers and assumes that the scaling factor is the quotient of their scaling factors.  In general, the first division requires rounding and therefore the result is not exact.

For example, division of 3456 scaled by 1/100 (34.56) and 1234 scaled by 1/1000 (1.234) yields the integer 3456÷1234 = 3 (rounded) with scale factor (1/100)/(1/1000) = 10, that is, 30.  As another example, the division of the first number by 155 implicitly scaled by 1/32 (155/32 = 4.84375) yields the integer 3456÷155 = 22 (rounded) with implicit scaling factor (1/100)/(1/32) = 32/100 = 8/25, that is 22×32/100 = 7.04.

If the result is not exact, the error introduced by the rounding can be reduced or even eliminated by converting the dividend to a smaller scaling factor.  For example, if ''r'' = 1.23 is represented as 123 with scaling 1/100, and ''s'' = 6.25 is represented as 6250 with scaling 1/1000, then simple division of the integers yields 123÷6250 = 0 (rounded) with scaling factor (1/100)/(1/1000) = 10.  If ''r'' is first converted to 1,230,000 with scaling factor 1/1000000, the result will be 1,230,000÷6250 = 197 (rounded) with scale factor 1/1000 (0.197).  The exact value 1.23/6.25 is 0.1968.