ABSTRACT
Rational numbers measure directed distances of certain points from zero in terms of some unit distance. The rational numbers become strongly associated with those points and we speak of them as if they are points, but they are, in fact, measures of distance. A unit of measure can always be divided up into finer and finer subunits so that you may take as precise a reading as you need. On a number line, on a graduated beaker, on a ruler or yardstick or meter stick, on a measuring cup, on a dial, or on a thermometer, some subdivisions of the unit are marked. Experience with fractions as measures entails a dynamic movement among an infinite number of stopping-off places along the number line, and helps students to build a sense of the density of rational numbers, a sense of order and relative magnitudes of rational numbers, and a richer understanding of precision in measurement.
