# rational number

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Related to rational number: real number, irrational number

## rational number:

see numbernumber,
entity describing the magnitude or position of a mathematical object or extensions of these concepts. The Natural Numbers

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their
.

## Rational Number

a number that can be expressed in the form of a fraction m/n, where m and η are integers and n ≠ 0. Since an integer m can be expressed as m/1, all integers are rational numbers. The operations of addition, subtraction, multiplication, and division (by nonzero divisors) can always be performed in the domain of rational numbers; thus, the rational numbers form a field. The basic rules of the operations over the rational numbers are given by the formulas

Rational numbers can also be represented in the form of finite decimals or infinite periodic decimals. Every irrational number can be included between two rational numbers, the difference between which can be made arbitrarily small.

## rational number

[′rash·ən·əl ′nəm·bər]
(mathematics)
A number which is the quotient of two integers.

## rational number

any real number of the form a/b, where a and b are integers and b is not zero, as 7 or 7/3
References in periodicals archive ?
Before proving this proposition, observe that the only rational numbers between 0 and 1 that do not satisfy the above conditions are 0,1,1/2,1/3 and 2/3.
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.
rational numbers and decimal expansions are synonyms again?
Johnson (1998) found that preservice elementary teachers have a gap in their rational number understanding and that they rely on the use of algorithms when approaching non-standard problems.
The proof begins with two arbitrary rational numbers M and N, where M = A/B N = C/D A, B, C and D are all integers.
In fact, roughly speaking, the sets constructed in [6,7] are Liouville numbers satisfying, in particular, that [mathematical expression not reproducible], for an infinite sequence of rational numbers [([p.
En route to a formulation for GCRD by means of the function G, think of a and b (likewise c and d) as the numerator and denominator, respectively, of a rational number.
Consequently, condition r [member of] Q cannot be fulfilled all time because of irrational numbers, which fill densely neighborhood of any rational number.
Moss and Case (1999) agreed that notation is one factor that could be linked to children's difficulties with fractions but they also pointed to several other complications: 1) Too much time is devoted to teaching the procedures of manipulating rational numbers and too little time is spent teaching their conceptual meaning, 2) Teachers do not acknowledge or encourage spontaneous or invented strategies, thereby discouraging children from attempting to understand these numbers on their own (Confrey, 1994, Kieren, 1992, Mack, 1993, Sophian & Wood, 1997) and, 3) When introduced, rational numbers are not sufficiently differentiated from whole numbers (e.
r], where r is a rational number, it was shown that the quantity [(-8).
In fact, the machine will compute with rational numbers only and this is related to an essential property of the constraints that can be employed in Prolog III; if a variable is sufficiently constrained to represent a unique real number then this number is necessarily a rational number.
Moreover, g has finite order if and only if [phi] is a rational number.

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