number axis

A straight line with a unique origin, a unique positive direction and a unique unit length is called a number axis. All rational numbers can be used.

Points on the number axis. You can also use the number axis to compare the sizes of two real numbers.

meaning

1) from the origin, the positive point on the ray corresponds to a positive number, the negative point on the ray corresponds to a negative number, and the origin corresponds to zero.

2) For the two numbers represented on the number axis, the number in the positive direction is greater than the number in the negative direction.

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

The number axis is a specific geometric figure; Origin, positive direction and length unit are the three elements of the shaft, and they are all indispensable.

key element

The straight line that defines the unique origin, positive direction and unit length is called the number axis.

If the points on the number axis represent imaginary numbers, two number axes need to form a rectangular coordinate system, and the sum of real numbers and imaginary numbers should be represented on a two-dimensional plane outside the two number axes.

Any rational number can be represented by a point on the number axis.

Generally, the right direction is the positive direction, and the points on the number axis correspond to any real number, including irrational numbers.

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App application

Compare sizes with the number axis

Generally speaking, when the number axis faces right, the number on the right is larger than the number on the left.

Corresponding thing

Two numbers represented by two points with the same distance from the origin but different signs are opposite numbers.

absolute value

Any distance from the origin is its absolute value. Similarly, the distance between two numbers on the number axis can also be expressed as the absolute value of the difference between the two numbers.

The absolute value of any number is nonnegative.

Using the number axis skillfully to calculate time

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, the time required for the second place is to 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, the meridian of 180 can be represented by two endpoints of this line segment, which can avoid crossing the date line and simplify the calculation.