The number axis is the product of the combination of number and shape. It refers to a straight line that uses points on a straight line to represent numbers, and mathematically specifies the origin, positive direction and unit length. The number axis meets the following requirements: take any point on the straight line to represent 0, which is called the origin; Generally speaking, the right (or upward) from the origin is the positive direction, and the left (or downward) from the origin is the negative direction.
The drawing method of the number axis is: draw a horizontal straight line, take any point on this straight line as the origin, and then determine the positive direction and unit length. The three elements of the number axis are indispensable, and there is only one positive direction. Generally speaking, the right direction is the positive direction, and the number axis has no points. When labeling numbers, numbers are generally labeled below the number axis, and letters representing points are written above the number axis.
The role of the number axis:
1, using the number axis can directly reflect the characteristics of the opposite number. Only two numbers with different symbols are reciprocal. As can be seen from the number axis, the two points representing the reciprocal, one on the left and the other on the right of the origin, are at the same distance from the origin (except 0).
2. The geometric meaning of absolute value can be explained by the number axis. On the number axis, the distance between the point corresponding to a number and the origin is called the absolute value of this number, which is the geometric meaning of absolute value. According to the geometric meaning of absolute value, the absolute value of any number is non-negative.
3. Use the number axis to compare the sizes of rational numbers. The numbers represented by the points on the number axis are all positive numbers on the right side of the origin and negative numbers on the left side of the origin; The number represented by two points on the number axis is always larger on the right than on the left. It is concluded that there is neither a maximum rational number nor a minimum rational number. There is no number with the largest absolute value, and the number with the smallest absolute value is 0.