Knowledge points related to negative numbers

1. The definition of negative numbers

1. All numbers learned before (except 0) are positive numbers, which means that the "+" in front of positive numbers can be omitted. !

2. The definition of negative numbers: adding "-" in front of a positive number is a negative number.

3. Negative numbers must be preceded by "-". If they are not preceded by "-" (there may be no sign or "+"), they are all positive numbers (except 0).

4. 0 is neither a positive number nor a negative number. It is the boundary between positive numbers and negative numbers.

2. The role of negative numbers

1. Negative numbers appear under the premise of artificially specifying the positive direction.

2. Negative numbers are often used to represent quantities that have the opposite meaning to positive numbers.

3. When choosing whether to express a positive number or a negative number, first check whether the positive direction is specified.

4. Generally, the amount with a positive connotation is expressed by a positive number, and the amount with a derogatory connotation is expressed by a negative number.

Example: 5° above zero is expressed as +5°C; 5° below zero is expressed as -5°C. An income of 2,000 yuan is expressed as +2,000 yuan; an expenditure of 500 yuan is expressed as -500 yuan.

3. The meaning of common negative numbers

(1) Negative numbers on the map:

On the topographic map of China, you can see that our country has the highest peak in the world - Mount Everest is marked 8848 on the map. There is a Turpan Basin in the northwest. It is marked -155 meters on the map. Can you tell me what 8848 meters and -155 meters mean? Who is the standard for these two heights?

　　(2) Income and expenditure

　　Income: 2600 yuan, ( ) Educational expenditure: 300 yuan ( ) Entertainment expenditure: 500 yuan ( ).

(3) Negative number in the elevator room

-What does the third floor mean? Who is it based on?

Starting from the school, go east It is positive, and it is negative when walking west. Xiao Ming walked +50m from the school, and then walked -100m. At this time, the distance between Xiao Ming and the school is ( ).

Food packages often indicate: "Net weight 500±5g," which means that the standard mass of the food is (), and the actual weight without bags is no more than () at most and at least no less than ().

4. Reading and writing of negative numbers

1. Reading: add "negative" in front of the reading

2. Writing: where Add "-" before writing a number

5. Understand the number axis

1. The elements of the number axis: positive direction (indicated by the arrow), origin (0 scale), unit length (scale ).

Positive direction: Determine the positive direction according to the meaning of the question. Generally, upward or right is the positive direction.

The origin: that is, the position of the number 0. It is generally determined according to the distribution of the represented numbers. If the positive and negative numbers that need to be represented are almost equal, the origin is in the middle of the number axis; if there are many more positive numbers than negative numbers, The origin is to the left; if there are many more negative numbers than positive numbers, the origin is to the right.

Unit length: The size of the distance between the scales is determined by the size to be expressed. If the number is too large, the distance between the scales can be appropriately smaller. If the number is too small, the distance between the scales can be appropriately larger. The unit length does not necessarily represent only 1 per tick.

2. Use the number axis to express the number

Represent the number on the given number axis: draw points on the corresponding scale according to the number.

For the representation of non-integers: further subdivide the scale. For example, if you need to divide the line segment between 0-1 into 3 equal parts, then the 2 equal parts will be the number.

For the representation of negative numbers: negative numbers are to the left of 0, and positive numbers are to the right of 0. Example: +3.5 is between 3 and 4, and -3.5 is between -3 and -4.

3. Compare numbers according to the number axis

All positive numbers are greater than negative numbers; all negative numbers are less than positive numbers

The numbers to the left of 0 are Negative numbers, the numbers to the right of 0 are all positive;

On the number axis, the numbers to the right are larger, and the numbers to the left are smaller;

Negative numbers are compared, and the negative sign is not considered. , the number with a large numerical part is small;

0 is greater than all negative numbers and less than all positive numbers. Negative number < 0 < Positive number

Taking the school as the starting point, walking eastward is positive and walking westward is negative. Xiao Ming walked +50m from school and then walked -100m. At this time, Xiao Ming left the school. The distance is ( ).

Food packages often indicate: "Net weight 500±5g," which means that the standard mass of the food is (), and the actual weight without bags is no more than () at most and at least no less than ().

4. How to read and write negative numbers

1. Reading: Add "negative" in front of the reading

2. Writing: where Add "-" in front of the written number