• Precision. How close is the representation to the exact value? Graphs are usually not very precise. With enough digits to the right of the decimal point, decimal representation can be as precise as desired.

Consider the following representations for one-half:

And one-half is the simplest fraction. Much more is involved in understanding and translating among representations of or rational numbers more generally. (See Box 3–9 for an example.)

Box 3–9 Translating Among Representations: An Example

Perhaps the deepest translation problem in pre-K to grade 8 mathematics concerns the translation between fractional and decimal representations of rational numbers. Successful translation requires an understanding of rational numbers as well as decimal and fractional notation—each of which is a significant and multifaceted idea in its own right. In school, children learn a standard way of converting a fraction such as to a decimal by long division.

The first written step of the long division is dividing 30 tenths by 8. After three divisions, the process stops because the remainder is zero. The quotient obtained, 0.375, is said to be a finite (or terminating) decimal because the number of digits is finite.

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