Consequently, all irrational roots of P have the form -a [+ or -] [e.sub.i][square root of D], i = 1, ..., t, where [e.sub.i] are distinct positive

rational numbers. If P is of odd degree, it has a rational root [alpha].

Elementary school math textbooks in Korea devote far more space to

rational number arithmetic and provide more practice problems than do U.S.

While the solution of the differential equation that is obtained by using the arbitrary values of nonnegative integer n gives the same geodesics as the two-parameter Weibull function, new function that defined nonnegative

rational numbers of n is derived for two-dimensional family of curve.

On the mathematical, cognitive, and instructional foundations of

rational numbers. In A.

(ii) for large values of K and exponent m being a

rational number the formula for S(x) is similar but D(x) takes the form

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.

The other text was Making Sense of Fractions, Ratios, and Proportions (NCTM 2002), the 64th yearbook from the National Council of Teachers of Mathematics (NCTM) that focused specifically on recent research related to issues with

rational numbers and offered us a wider view of the existing research.

Leaving the realm of integers, we remind him as well of the concept of

rational number as a quotient p/q, q[not equal to]0 with integers p and q in lowest terms and known facts such as (i) integers can be considered as

rational numbers, (ii) the decimal expansion of a

rational number always either terminates after finitely many digits or begins to repeat the same finite sequence of digits over and over and again, (iii) any repeating or terminating decimal represents a

rational number.

Throughout this paper, we use R, [R.sup.+], [R.sup.-], Q, Z, and [Z.sup.+] to denote real numbers, positive real numbers, negative real numbers,

rational numbers, integers, and positive integers, respectively.

Then there exist

rational numbers [[lambda].sub.0], ..., [[lambda].sub.p], not all 0, such that