# chickadee » scheme » rationalize

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rationalize x yprocedure

Rationalize returns the simplest rational number differing from x by no more than y. A rational number r[1] is simpler than another rational number r[2] if r[1] = p[1]/q[1] and r[2] = p[2]/q[2] (in lowest terms) and |p[1]| < |p[2]| and |q[1]| < |q[2]|. Thus 3/5 is simpler than 4/7. Although not all rationals are comparable in this ordering (consider 2/ 7 and 3/5) any interval contains a rational number that is simpler than every other rational number in that interval (the simpler 2/5 lies between 2/7 and 3/5). Note that 0 = 0/1 is the simplest rational of all.

```(rationalize
(inexact->exact .3) 1/10)          ===> 1/3    ; exact
(rationalize .3 1/10)                ===> #i1/3  ; inexact```