Editing Fixed-point arithmetic (section)

===Exact values===

Any binary fraction ''a''/2<sup>''m''</sup>, such as 1/16 or 17/32, can be exactly represented in fixed-point, with a power-of-two scaling factor 1/2<sup>''n''</sup> with any ''n'' ≥ ''m''.  However, most decimal fractions like 0.1 or 0.123 are infinite [[repeating fraction]]s in base 2. and hence cannot be represented that way.

Similarly, any decimal fraction ''a''/10<sup>''m''</sup>, such as 1/100 or 37/1000, can be exactly represented in fixed point with a power-of-ten scaling factor 1/10<sup>''n''</sup> with any ''n'' ≥ ''m''.  This decimal format can also represent any binary fraction ''a''/2<sup>''m''</sup>, such as 1/8 (0.125) or 17/32 (0.53125).

More generally, a [[rational number]] ''a''/''b'', with ''a'' and ''b'' [[relatively prime]] and ''b'' positive, can be exactly represented in binary fixed point only if ''b'' is a power of 2; and in decimal fixed point only if ''b'' has no [[prime]] factors other than 2 and/or 5.