Turn left | turn right

concept

In mathematics, numbers can be represented by points on a straight line, which is called a number line, and it satisfies the following conditions: (1) Take any point on the line to represent 0, and this point is called the origin; (2) Generally, from the origin to the right (or upward) is the positive direction, and from the origin to the left (or downward) is the negative direction; (3) Choose an appropriate length as the unit length, and take a point every other unit length on the straight line from the origin to the right, indicating 1 (1 unit length to the right), 2 (2 unit lengths to the right), 3 (3 unit lengths to the right), …; From the origin to the left,-1 (left 1 unit length), -2 (2 unit lengths to the left) and -3 (3 unit lengths to the left) are expressed in a similar way.

On the number axis, besides the number 0, you need to represent any rational number that is not 0. According to the sign of this number, determine which side of the number axis it is on (usually positive numbers are on the right side of the origin and negative numbers are on the left side of the origin), then determine that it is several unit lengths away from the origin in the corresponding direction, and then draw the corresponding point.

Fold and edit the geometric meaning of this paragraph.

The number axis is a specific geometric figure; The origin, positive direction and three elements of the unit length scale axis are indispensable.

1) Starting from the origin, the point in the positive direction (positive half axis) on the ray corresponds to a positive number, the point in the opposite direction (negative half axis) on the ray corresponds to a negative number, and the origin corresponds to zero.

2) Of the two numbers represented on the number axis, the number in the positive direction is always greater than the number on the other side.

3) Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than all negative numbers.

Note: The unit length refers to taking an appropriate length as the unit length. For example, 2m can be taken as the unit length "1", so 4m is two unit lengths. The unit of length refers to meters, centimeters, millimeters and other units that express length.

The two should not be confused.

There is a one-to-one correspondence between points and numbers on the number axis. Any number, including imaginary number, can be represented by a point on the number axis. )

The positive direction of the number axis is generally to the right, but the possibility of turning to the left is not ruled out. The closer to the positive direction, the greater the number, and the farther away from the positive direction, the smaller the number.

When drawing a number of axes, it is generally necessary to draw a horizontal line and a positive direction first, then draw a zero, and then draw a unit length according to the meaning of the question.

Fold and edit the reverse side of this paragraph.

Numbers with only two different signs are called reciprocal, and one of them is called reciprocal of the other.

The inverse of (a≠0)a is -a, and the inverse of 0 is 0.

Fold and edit the absolute value of this paragraph.

The distance between the point representing a number on the number axis and the origin is called the absolute value of this number.

The absolute value of a positive number is itself, and the absolute value of a negative number is its inverse. The absolute value of 0 is 0.

Formula |a|=?

If a is greater than 0, the absolute value of a is equal to a;

If a is equal to 0, the absolute value of a is equal to 0;

If a is less than 0, the absolute value of a is equal to-a.

Attribute: The absolute value is non-negative.

Rational number comparison size:

All positive numbers are greater than 0, 0 is greater than all negative numbers, and positive numbers are greater than all negative numbers.

Note: the number on the right side of the axis is always greater than the number on the left. When comparing two negative numbers, the absolute value is larger, but smaller.

Fold and edit the calculation time of this paragraph.

On the number axis, there is a segment on the number axis that represents the global longitude. The two ends of this line segment represent the longitude 180, and the midpoint of the line segment represents the longitude 0, so that the longitude positions all over the world can be represented on this line segment. The direction of the arrow represents the direction of the earth's rotation. So the longitude from east longitude 0 to east longitude180 is east longitude, and the rightmost time zone is east longitude12, which is the earliest. The longitude from 0 to 180 is the west longitude, the leftmost time zone is the west 12 area, and the time is the latest, and the difference between the east and the west 12 area is just 24 hours. On this number axis, the farther to the right, the earlier the time, and the greater its value, which is consistent with the mathematical significance of the number axis. Therefore, if the time of location B in figure 1 is known, but the time of location A is needed, and location A is on the right side of location B, then add them, that is, the time of location A is equal to the time of location B plus the time difference between location A and location B; On the other hand, it requires the time of the second place, and the second place is on the left of the first place. By subtraction, it can be recorded as "right plus left minus". At the same time, because the direction of the number axis represents the rotation direction of the earth from west to east, in this sense, it can also be recorded as "East plus West minus". In this way, it is not easy to make mistakes by combining the choice of addition and subtraction with the mathematical meaning of time and number axis. In addition, using two endpoints of this line segment to represent longitude 18 and 0 meridian of standard chemical industry can avoid crossing with international date line, thus simplifying calculation.

The function of 1. number axis

(1) The straight line defining the origin, positive direction and unit length is called the number axis.

There are two contents here: first, the three elements of the number axis: the origin, the positive direction and the unit length are indispensable; Second, these three elements are stipulated.

(2) The number axis can visually represent numbers, and the points on the number axis correspond to real numbers one by one, that is, each real number can be represented by a point on the number axis.

(3) Compare sizes, with 0 as the center, and the number on the right is greater than the number on the left!

This involves the completeness of real numbers. Rational numbers are incomplete, that is, there is a gap between any two rational numbers, while real numbers are complete, and the number between any two real numbers is still real numbers.

Use of folding to edit this paragraph

Mathematically, the number axis is a one-dimensional figure, and integers are evenly distributed on a line as special points. The number axis is a straight line that defines the origin, direction and unit length. The origin, direction and unit length are called the number axis. It is usually used to help teach simple addition or subtraction (especially when there are negative numbers in the operation).

In most cases, the number axis is represented as horizontal (although this is not necessary). It is divided into two symmetrical parts by the origin 0. Usually positive numbers are on the right of 0 and negative numbers are on the left of 0. All real numbers correspond to points on the number axis.