Rational number is a must for the senior high school entrance examination. How do students master the knowledge of rational numbers? Below I will share the knowledge of rational number related test sites for you, hoping to have a reference for your preparation!

1. rational number:

(1) Any number that can be written in form is a rational number. Positive integers, 0 and negative integers are collectively referred to as integers. Positive and negative scores are collectively called scores; Integers and fractions are collectively called rational numbers. Note: 0 is neither positive nor negative; -a is not necessarily negative, and +a is not necessarily positive; Not a rational number;

(2) Classification of rational numbers: ① ②

2. Number axis: The number axis is a straight line that defines the origin, positive direction and unit length.

3. The opposite number:

(1) There are only two numbers with different signs, and we say that one of them is opposite to the other; The antonym of 0 is still 0;

(2) The sum of enantiomers is 0a+b=0a, and B is the enantiomer.

4. Absolute value:

(1) The absolute value of a positive number is itself, the absolute value of 0 is 0, and the absolute value of a negative number is its inverse; Note: the absolute value means the distance between the point representing a number on the number axis and the origin;

(2) The absolute value can be expressed as: or; The problem of absolute value is often discussed in categories;

5. Rational number ratio: (1) The greater the absolute value of a positive number, the greater the number; (2) Positive numbers are always greater than 0 and negative numbers are always less than 0; (3) Positive numbers are greater than all negative numbers; (4) The absolute values of two negative numbers are larger than the size, but smaller; (5) Of the two numbers on the number axis, the number on the right is always greater than the number on the left; (6) large number-decimal number >; 0, decimal-large number < 0.

6. Reciprocal: Two numbers whose product is 1 are reciprocal; Note: 0 has no reciprocal; If a? 0, the reciprocal is; If ab= 1a and b are reciprocal; If ab=- 1a and b are negative reciprocal.

7. The rational number addition rule:

(1) Add two numbers with the same symbol, take the same symbol, and add the absolute values;

(2) Add two numbers with different symbols, take the symbol with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value;

(3) Adding a number to 0 still gets this number.

8. Arithmetic of rational number addition:

The commutative law of (1) addition: a+b = b+a; (2) The associative law of addition: (a+b)+c=a+(b+c).

9. Rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number; That is, a-b=a+(-b).

10. rational number multiplication rule:

(1) Multiply two numbers, the same sign is positive, the different sign is negative, and the absolute value is multiplied;

(2) Multiply any number by zero to get zero;

(3) When several numbers are multiplied, one factor is zero and the product is zero; Each factor is not zero, and the sign of the product is determined by the number of negative factors.

1 1. Arithmetic of rational number multiplication:

(1) The commutative law of multiplication: ab = ba(2) The associative law of multiplication: (AB) C = A (BC);

(3) Distribution law of multiplication: a(b+c)=ab+ac.

12. rational number division rule: dividing by a number is equal to multiplying the reciprocal of this number; Note: Zero cannot be divisible.

13. Power Law of Rational Numbers:

(1) Any power of a positive number is a positive number;

(2) The odd power of a negative number is a negative number; Even the power of negative numbers is positive; Note: When n is positive odd number: (-a)n=-an or (a-b)n=-(b-a)n, when n is positive even number: (-a)n=an or (a-b) n = (b-a) n. 。

14. Definition of power:

(1) The operation of seeking common ground factor product is called power;

(2) In power, the same factor is called base, the number of the same factor is called exponent, and the result of power is called power;

15. scientific notation: write a number greater than 10 as a? 10n, where a is an integer with only one bit. This notation is called scientific notation.

16. Approximation precision: a divisor rounded to that bit, that is, the divisor is accurate to that bit.

17. Significant digits: All digits from the first non-zero digit on the left to the exact digit are called significant digits of this approximation.

18. Mixed algorithm: multiply first, multiply then divide, and finally add and subtract.

This chapter requires students to correctly understand the concept of rational numbers, and understand the meanings of positive and negative numbers, antonyms and absolute values on the basis of real life and learning the number axis. Focus on solving practical problems with the algorithm of rational numbers.

An important reason for the development of experiential mathematics is the actual needs of life. Stimulate students' interest in learning mathematics, teachers cultivate students' ability of observation, induction and generalization, and enable students to establish a correct sense of numbers and the ability to solve practical problems. When teaching this chapter, teachers should create more situations to fully reflect the main position of students' learning.

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