First, knowledge combing

Knowledge point 1: the concepts of positive numbers and negative numbers: we call numbers such as 3, 2, +0.5 and 0.03% positive numbers, all of which are numbers greater than 0; Numbers like -3, -2, -0.5 and -0.03% are called negative numbers. Are all numbers less than 0. 0 is neither positive nor negative. We can use positive numbers and negative numbers to represent quantities with opposite meanings.

Knowledge point 2: the concept and classification of rational numbers: integers and fractions are collectively called rational numbers. There are two main classifications of rational numbers:

Note: Both finite decimals and infinite cyclic decimals can be regarded as fractions.

Knowledge point 3: the concept of number axis: the straight line with the origin, positive direction and unit length as follows is called number axis.

Knowledge point 4: the concept of absolute value:

(1) Geometric meaning: The distance from the point representing A on the number axis to the origin is called the absolute value of the number A, and it is recorded as | a |

(2) Algebraic significance: the absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of zero is zero.

Note: The absolute value of any number is greater than or equal to 0 (i.e. non-negative).

Knowledge point 5: the concept of reciprocal:

(1) Geometric meaning: The number represented by two points on both sides of the origin with the same distance is called reciprocal;

(2) Algebraic meaning: Two numbers with different signs but equal absolute values are called reciprocal. The reciprocal of 0 is 0.

Knowledge point 6: Comparison of rational numbers:

The basic principle of rational number size comparison: positive numbers are all greater than zero, negative numbers are all less than zero, and positive numbers are greater than negative numbers.

Comparison of rational numbers on the number axis: the number on the right is always greater than the number on the left.

Comparison between rational number and absolute value: two positive numbers, the positive number with larger absolute value is larger; Of the two negative numbers, the one with larger absolute value is smaller.

Knowledge point 7: rational number addition rule:

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

(2) When two numbers with different signs are added and the absolute values are equal, the sum is 0; When the absolute values are not equal, take the sign of the addend with larger absolute values and subtract the addend with smaller absolute values from the addend with larger absolute values;

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

Knowledge point 8: rational number addition algorithm:

Additive commutative law: When two numbers are added, the position of the addend is reversed and the sum remains the same.

Law of addition and association: 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.

Knowledge point 9: rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number.

Knowledge point 10: mixed operation of rational number addition and subtraction: according to the law of rational number subtraction, all addition and subtraction operations can be unified into addition operations, and then brackets and plus signs are omitted, and calculations are made by using the law of addition and the law of addition operation.

Knowledge point 1 1: multiplication and division method

1. multiplication rule

2. Division rule

3. How to determine the symbol of the final result of multiplication and division of multiple non-zero numbers?

Knowledge point 12: countdown

1. Reciprocity concept

2. How to find the reciprocal of a number? (Note the difference with the opposite number)

Knowledge point 13: motivation

1. What is the concept of power and the result of power?

Step 2 know the cardinal number, index

3. The power of any positive number is _ _ _ _ _ _ _, and the power of any zero is _ _ _ _ _ _ _

The even power of a negative number is _ _ _ _ _ _ _ and the odd power is _ _ _ _ _ _ _

Knowledge point 14: mixed computing

Note: the order of operation is the key, and the calculation should be carried out in strict order.

Knowledge points 15: scientific notation

The concept of scientific notation? Pay attention to the range of a.