Fixnum#to_r is not mentioned here, it was introduced since ruby 1.9. It converts Fixnum into rational form. Below are examples of its uses. This also can give exact division as long as all the numbers used are Fixnum.
a = 1.to_r #=> (1/1)
a = 10.to_r #=> (10/1)
a = a / 3 #=> (10/3)
a = a * 3 #=> (10/1)
a.to_f #=> 10.0
Example where a float operated on a rational number coverts the result to float.
a = 5.to_r #=> (5/1)
a = a * 5.0 #=> 25.0