Knowledge network:
Concept, definition:
1 and numbers greater than 0 are called positive numbers.
2. Numbers with negative sign "-"in front of positive numbers are called negative numbers.
3. Integers and fractions are collectively called rational numbers.
People usually use points on a straight line to represent numbers. This straight line is called the number axis.
5. Take any point on the straight line to represent the number 0. This point is called the origin.
6. Usually, the distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A. ..
7. From the definition of absolute value, we can know that the absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0.
8. Positive numbers are greater than 0, 0 is greater than negative numbers, and positive numbers are greater than negative numbers.
9, two negative numbers, the absolute value is big but small.
10, rational number addition rule
(1) Add two numbers with the same sign, take the same sign, and add the absolute values.
(2) Add two numbers with different absolute values, take the negative sign of the addend with larger absolute value, subtract the number with smaller absolute value from the number with larger absolute value, and add the two numbers with opposite numbers to get 0.
(3) When a number is added to 0, the number is still obtained.
1 1. In rational number addition, two numbers are added, the position of the addend is exchanged, and the sum is unchanged.
12. rational number addition, when three numbers are added, the first two numbers are added first, or the last two numbers are added first, and the sum is unchanged.
13, rational number subtraction rule
Subtracting a number is equal to adding the reciprocal of this number.
14, rational number multiplication rule
Multiply two numbers, the same sign is positive, the different sign is negative, and then multiply by the absolute value.
Any number multiplied by 0 is 0.
15, and rational numbers: two numbers whose product is 1 are reciprocal.
16. In general rational number multiplication, two numbers are multiplied, and the exchange factor and product are in the same position.
17, multiply three numbers, first multiply the first two numbers, or multiply the last two numbers, and the products are equal.
18. Generally speaking, a number multiplied by the sum of two numbers is equivalent to multiplying this number by these two numbers respectively, and then adding the products.
19, rational number division rule
Dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.
20. Divide two numbers, the same sign is positive, and the different sign is negative, divided by the absolute value. Divide 0 by any number that is not equal to 0 to get 0.
2 1, the operation of finding the product of n identical factors is called power, and the result of power is called power. In an, a is called basenumber and n is called exponeht.
22. According to the multiplication rule of rational numbers, we can draw a conclusion.
The odd power of a negative number is negative and the even power of a negative number is positive.
Obviously, any degree of a positive number is positive, and any degree of 0 is 0.
23, do rational number mixed operation, should pay attention to the following operation order:
(1) Multiply first, then multiply and divide, and finally add and subtract;
(2) the same layer operation, from left to right;
(3) If there are brackets, do the operation in brackets first, and then follow the brackets, brackets and braces in turn.
24. Numbers greater than 10 are expressed in the form of a× 10n (where a is a number with only one integer and n is a positive integer), and scientific counting methods are used.
25. Close to the actual number, but still different from the actual number. This figure is an approximation.
26. From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number.