Meaning of 1, positive number, negative number and 0.

Numbers-positive numbers, negative numbers and 0-are produced due to the needs of production and life.

Numbers greater than (1) are called positive numbers, and the "+"sign before positive numbers is usually omitted.

(2) The number added before a positive number is called a negative number.

(3)0 is neither nor; 0 not only means "no", but also means, for example, that the altitude of sea level is 0.

Note: Both positive and negative numbers consist of sign and absolute value.

[1] Among the known numbers-7,2.1,0,-1/3, 13, there are positive numbers; Negative numbers have; Numbers that are not negative numbers are negative numbers; Non-positive numbers are positive numbers.

Note: Numbers that are not negative numbers are called non-negative; A non-positive number is called a non-positive number.

2. Use positive numbers and negative numbers to represent quantities with opposite meanings.

Positive and negative numbers are used to represent quantities with opposite meanings. For example, +2 yuan indicates that the stock is rising in 2 yuan, -3 yuan indicates.

Add a "-"sign before a number to get the same meaning as the original number.

[2] The following statement is wrong.

① The antonym of 6℃ above zero is only 6℃ below zero;

② Income and expenditure are a pair of quantities with opposite meanings;

(3) Shipment of 5 tons and income from 5 yuan are a pair of quantities with opposite meanings.

The quantity of opposite meaning contains two elements: one is their meaning, and the other is that they both have and must be.

(3) If 5℃ above zero is recorded as +5℃, then 5℃ below zero is recorded as ()

a 、-5℃B 、- 10℃ D 、- 5℃

3. Rational Numbers and Related Concepts

(1) are collectively referred to as integers;

(2) collectively referred to as scores;

(3) collectively known as rational numbers.

Note: Both finite decimals and infinite cyclic decimals can be converted into fractions.

4. Classification of rational numbers

(1) By definition:

(2) According to the nature:

Note: Classification should be based on the same standard to avoid duplication or omission.

Second, role model guidance

Example 1 The following statements: ① All integers are positive numbers; ② All positive numbers are integers; (3) Numbers in primary school are all positive numbers; ④ The score is a rational number; ⑤ All rational numbers are positive except negative numbers. Among them, the number of correct statements is ()

a，0 B， 1 C，3 D，4

Example 2 Fill in the following figures in the corresponding brackets: 7, -9.25, -9/ 10, -30 1,

4/27,-3.5,0,2, 1 1/2,-7, 1.25,-7/3,-3,-3/4.

Positive number {}

Negative number {}

Negative integer {}

Positive score {}

Non-negative integer {}

Non-positive score {}

Example 3 A school conducted a push-up test for seventh-grade boys, and the results of eight boys are shown in the following table:

Student ID 1 2 3 4 5 6 7 8

Achievement (individual) 7 8 5 2 3 7 4 6

Please specify a meaningful quantity as positive, and re-list positive and negative numbers to represent the achievements of these eight students.

Third, practice is improved.

Solid foundation

1. If the deposit is positive, a savings office receives four transactions within 1 hour: deposit of 2000 yuan, withdrawal of 1200 yuan, deposit of 400 yuan and withdrawal of 800 yuan, which are represented by positive and negative numbers respectively.

2. The following statement: ① The meaning of zero only means no; ②0 is the smallest positive integer; ③0 is neither positive nor negative; ④0 is an even number and a natural number. The correct one is ()

a、①③④

b、①②③④

③④

d、②④

3. Among the following quantities, the quantity with opposite meaning is ().

A, the crane rises 5 meters and moves 3 meters to the right.

B, go forward and backward

C. Earn 40 Jin of corn and borrow 40 Jin of corn.

D, deposit 30,000 yuan and withdraw 20,000 yuan.

4. If 16 kWh is saved as+16, 6 kWh is wasted.

5. If the hands on the clock rotate 30 degrees clockwise and record as +30 degrees, the meaning of -20 degrees is.

6. If the water level drops by 3 meters and is marked as -3 meters, then the water level rises by 4 meters and is marked as ().

a， 1m

B, 7 meters

c，+4m

Diameter,-7m

7. If -4m means that the object moves 4m to the west, then +2m means that the object is stationary.

8, negative numbers and integers.

9, the following statement is wrong ()

Positive integer must be a natural number

B, natural number must be a positive integer

C and 0 are both integers and rational numbers.

D, finite decimals are also fractions

10, a food package was marked with "net content of 385 5 grams", and the acceptable content of this bag of food ranged from grams to grams.

1 1, go west-100 meters, which can be said to be ()

A, go west100m, and go east100m.

C, walk 200 meters west and 200 meters east.

12 and -7 belong to the number set (write the names of the three number sets).

13. Fill in the appropriate numbers on the horizontal line according to certain rules: -23,-18,-13.

14. Fill in the following figures in the corresponding brackets:

-4,5, ,- ,0,-2 1 , ,-0.03003。

Negative integer {}

Score {}

Non-negative number {}

Non-positive score {}

15, the school conducted a standing long jump test for junior one boys, and the standard was that they could jump 1.7m or more. The number of centimeters exceeding 1.7m is represented by a positive number, and the number of centimeters less than 1.7m is represented by a negative number.

The scores of boys in the first group 10 are as follows (in cm):

+2 -4 0 +5 +8 -7 0 +2 + 10 -3

(1) What is the farthest distance and the nearest distance?

(2) How many students in the first group reached the standard? What is the compliance rate?

Improve ability

16, the height of a submarine is-80m, and its dive height10m is recorded as.

17, Xiaoming is taller than Xiaogang-5 ㎝ means _ _ _ _ _ _ _.

18, the following statement is true ()

A has the smallest natural number and the smallest integer.

B, there is no minimum positive number, but there is a minimum positive integer.

C, there is no smallest negative number, but there is the largest negative number.

D and 0 are the smallest rational numbers.

19, the number of two groups with common parts is ().

I. Positive integer set and negative integer set

B, integer set and fraction set

C, negative set and integer set

D, negative score set and positive score set

20. The average math score of a class is 80. If the score is above 80 points, 85 points will be recorded as +5 points, and a classmate's math score will be 78 points, which should be recorded as ().

A, +2 points B, -7 points C, -2 points D, +7 points.

2 1. When the time difference between Paris and Beijing is -7 (a positive number means that the same moment is several hours earlier than Beijing time), if Beijing time is July 2 14: 00, then Paris time is ().

1. July 2, 2 1 year.

B, July 2 17: 00

C, at 5 o'clock on July 2

D, July 2 at 7 o'clock.

22. Fill in the appropriate numbers on the horizontal line according to certain rules: 1,-4,9,-16,25,,.

23. Fill in the following rational numbers in the corresponding circles:

-0.3,0,- 100,3.7,99.9,- 15/2, 10, ,2/3。

24. If the height of the desk is 2㎜ higher than the standard height and recorded as +2㎜, then what is recorded as 3㎜ lower than the standard height? There are five desks at present. Compared with the standard height, their dimensions are+1mm,-1mm, +3mm and-1.5mm respectively. If it is stipulated that the height of desks should not exceed 2mm and should not be less than 2mm, then the above five desks are all qualified.

Exploration and innovation

25. The standard price of a commodity is 400 yuan, but with the change of seasons, the price of the commodity can fluctuate by 5%.

(1) What does 5% mean?

(2) Please work out the highest and lowest prices of the goods;

(3) A merchant set the retail price of goods in 450 yuan and was punished by the price department. Please analyze the reasons for the punishment.