What are the concepts of rational numbers,,, what are the concepts of rational numbers?

The concept of rational numbers contains the principles and methods of classification of rational numbers, the concepts and characteristics of opposite numbers, number lines, and absolute values.

1. Classification of rational numbers: rational numbers include integers and fractions, integers include positive integers, 0 and negative integers, and fractions include positive fractions and negative fractions. The principle of "classification": (1) proportionality (no duplicate, no omission); (2) There are standards.

2. Non-negative numbers: a collective term for positive numbers and zeros.

3. Opposite number:

1) Definition: If the sum of two numbers is 0, then the two numbers are opposite to each other.

2) The formula for finding the opposite number: the opposite number of a is -a.

3) Properties: a≠0, a≠-a;

The position of a and -a on the number axis is symmetrical with respect to the origin;

The sum of two opposite numbers is 0 and the quotient is -1.

4. Number axis: definition ("three elements"): a straight line with origin, positive direction, and unit length is called the number axis.

Function: (1) Visually compare the magnitude of real numbers;

2) Clearly reflect the meaning of absolute value;

3) All rational numbers can be represented on the number line, and all irrational numbers can be represented on the number line, so some points on the number line represent rational numbers, some represent irrational numbers, and the points on the number line are one-to-one correspondence with real numbers.

5. Absolute value: (1) Algebraic definition: the absolute value of a positive number is its itself, the absolute value of 0 is its itself, and the absolute value of a negative number is its opposite.

2) Geometric definition: The geometric meaning of the absolute value of the number a is the distance from the point to the origin corresponding to the real number a on the number line.

What is the concept of a rational number.

Rational numbers are integers (positive integers.

0, negative integer) and fractions. Positive integers and positive fractions are collectively called positive rational numbers, and negative integers and negative fractions are collectively referred to as negative rational numbers. Therefore, the number of rational numbers in the set of rational numbers can be divided into positive rational numbers, negative rational numbers, and zeros.

Since any integer or fraction can be reduced to a decimal cyclic decimal number.

Conversely, every decimal cyclic decimal can also be reduced to an integer or fraction, so a rational number can also be defined as a decimal cyclic decimal number.

Rational numbers are a collective term for integers (positive integers, 0s, negative integers) and fractions, and are a collection of integers and fractions.

An integer can also be thought of as a fraction with a denominator of one. Real numbers that are not rational numbers are called irrational numbers, i.e., the fractional part of an irrational number is an infinite number that is not cyclical. It is one of the important contents in the field of "number and algebra", which has a wide range of applications in real life, and is the basis for continuing to learn real numbers, algebraic formulas, square dust quarrels, inequalities, Cartesian coordinate systems, functions, statistics and other mathematical content and related subject knowledge.

The set of rational numbers can be represented by the uppercase black orthography symbol q. But q does not mean rational numbers, and rational numbers and rational numbers are two different generalized hail attendants. A rational number set is a set of elements that are all rational numbers, while a rational number is a set of all the elements in a rational number set.

Origin of the name

The name "rational number" is incomprehensible, and rational numbers are no more "reasonable" than other numbers. In fact, it seems to be a translation error. The term rational number came from the West and is rational number in English, and rational usually means "rational".

In modern times, China translated Western scientific works into "rational numbers" based on the Japanese translation method. However, in ancient Greece, the English root of this word ** is ratio, which means ratio (the root here is in English, and the Greek meaning is the same). Therefore, the meaning of this word is also very obvious, that is, the "ratio" of integers.

In contrast, an "irrational number" is a number that cannot be accurately expressed as the ratio of two integers, and it is not unreasonable.

The above content reference: Encyclopedia - Rational Numbers.