Considering the existence of two complementary fractals on the sets of rational and irrational numbers accordingly [17], the probability that small variations (fluctuations) lead to coincidences between irrational and

rational numbers of small quotients is minimum.

Transition probabilities of the chain X are clearly

rational numbers so the components of [[pi].sup.(n)], as a solution of a linear system of rational equations, are

rational numbers.

Percents and proportion at the center: Altering the teaching sequence for

rational number. In Making Sense of Fractions, Ratios, and Proportions (109-120), edited by B.

Pr.: Right, but is it another way of understanding a decimal expansion independent of from where it comes from, let us say, from a

rational number and the associated process of repeated division?

Heuer:

Rational numbers generated by two integers, Am.

Partitioning: The emergence of

rational number ideas in young children.

I think we will come up with a

rational number that will be agreeable to all, or at least to those that really want to see it through."

The data reveals that preservice teachers apply well-ingrained whole number rules, instead of weakly understood fraction and decimal concepts, to draw false conclusion about

rational number representations, such as 0.45 is greater than 0.5 because 45 is greater than 5 (Ball, 1990).

These problems will test his understanding of

rational number (i.e., quotients that owe their existence to the ideas of unit fractions (1/b)).

If [Theta] is a

rational number A/B in lowest terms, it is easy to see that there are at most B distinct points generated.