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The position of rational number ABC on the number axis is shown in the figure, then the size relationship of a, negative a, B, negative B, C, negative C, 0 is?
What about the picture?
You can draw the position of their opposite numbers according to the position of a, B and C, and then you can compare the sizes. The one on the right is larger than the one on the left
The positions of a, B and C on the number axis are known as shown in the figure. Compare the sizes of a + B, B + C and C-B and connect them with ">"
∵ according to the position of B and C on the number axis, a < B < 0 < C, ∵ a + B < A, B < B + C < 0, C-B > 0, ∵ a + B < B + C < c-b
Use the number axis to find the distance between the points represented by each of the following logarithms on the number axis
(1) 3 and - 2.2 (2) 4 1 / 2 and 2 1 / 4 1 (3) - 4 and - 4.5 (4) - 3 1 / 2 and 2 1 / 3
(1)|3-(—2.2)|=5.2
(2) |4 1 / 2-2 1 / 4| = 9 / 4
（3）|—4-(—4.5)|=0.5
(4) | - 3 1 / 2-2 1 / 3 | = 35 / 6
The distance between two points on the number axis is equal to the absolute value of the difference between the two points
Please observe the logarithm of - 0.5 and 0.5, - 3 and 3 on the number axis. Can you tell us some of their characteristics
-0.5 and 0.5 are opposite numbers - 3 and 3 are opposite numbers
Find out the distance between the corresponding points of the following logarithms on the number axis: (1) 3 and - 2 (2) 2 and 4.5 (3) - 4 and - 1.5 (4) - 31 / 3 and 22 / 3, where - 31 / 3 is negative three and one-third. Can you find out the relationship between the distance and the difference between the two numbers? If A.B points on the number axis indicate the rational number A.B, please use the formula containing A.B to express the distance d between the two points of A.B. please explain the reason
1.5
2.2.5
3.2.5
4.32/3
Distance = the absolute value of the difference between the two numbers
d=|a-b|
Find the distance between the corresponding points of the following logarithm on the number axis
-3.5 and 2 and 1 / 3
namely
-3.5 → 2 and 1 / 3 distance
If the distance is the sum of absolute values, then the distance between - 3.5 and 2 / 3 is the absolute value of - 3.5 + 2 / 3, that is, 3 / 1 / 2 + 2 / 1 / 3, then 5 / 5 / 6
Is the sentence "all the points on the number axis represent real numbers"?
No, the definition of the number axis specifies the origin. The straight line in the positive direction and unit length is called the number axis. All real numbers can be represented by the points on the number axis. Imaginary numbers can be represented by the vertical axis on the number axis
How to represent real numbers on the number axis?
When I attended the lecture, I neglected I'm not serious
I checked on the Internet and found that the expressions of root 8 and root 5 are somewhat different. Why do some draw circles, squares and rectangles on the number axis?
Please answer for me, thank you. By the way, tell me how to express real number on the number axis
Thank you very much
To represent real numbers on the number axis is to use Pythagorean Theorem A ^ 2 + B ^ 2 = C ^ 2
Drawing circles, squares and rectangles is an auxiliary method. In fact, the core is Pythagorean theorem
For example, root 8 can be divided into root (2 ^ 2 + 2 ^ 2) to draw a square with side length of 2, and its diagonal is root 8. Similarly, root 5 can be divided into root (1's square + 2's Square), that is, to draw a rectangle with length of 2 and width of 1, and its diagonal is root 5
How to represent real numbers on the number axis?
For example:__
/3
for instance
Root 3
For example, root 3
Well In the first quadrant, take two unit lengths as the bottom and one unit length as the height, and connect them into a right triangle ABC. At this time, the hypotenuse is root sign 3. Use a compass to measure the length. Take the origin 0 as the center of the circle, root sign 3 as the radius, draw an arc intersection, and the x-axis is point D. at this time, OD is root sign 3 (that's what I know...)
How to express real numbers on the number axis?
All the points on the number axis are real numbers, and each point on the number axis corresponds to a real number
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- 11. The position of ABC three numbers on the number axis is shown in figure 2.3-2. The number axis c0ab is simplified as | a | / A + | B | / B + | / C | / C!
- 12. The three elements of the number axis are______ 、______ 、______ ．
- 13. Given that points a and B are on both sides of the origin on the number axis, their corresponding numbers are - 4,3x-5 / 2x + 2, and the distances from points a and B to the origin are equal, find the value of X
- 14. As shown in the figure, it is known that the number represented by point a on the number axis is 6, B is a point on the number axis, and ab = 10. Starting from point a, the moving point P moves uniformly to the left along the number axis at the speed of 6 unit lengths per second, and the movement time is t (T > 0) seconds (1) (1) write the number represented by point B on the number axis______ The number represented by point P______ (expressed by an algebraic expression containing T); ② m is the midpoint of AP and N is the midpoint of Pb. Does the length of segment Mn change during the movement of point P? If it changes, please explain the reason; if it doesn't change, please draw a graph and find out the length of line Mn; (2) moving point Q starts from point a and moves left uniformly along the number axis at the speed of 1 unit length per second; moving point R starts from point B and moves left uniformly along the number axis at the speed of 43 unit length per second; if P, Q and R start at the same time, when point P meets point R, it immediately returns to point Q Then, what is the unit length of the journey from the start to the stop of point P?
- 15. Points a and B are the corresponding points of numbers - 3 and - 12 on the number axis respectively. If line AB moves to the right along the number axis to a ′ B ′ and the number corresponding to the midpoint of line a ′ B ′ is 3, then the number corresponding to point a ′ is______ The distance that point a moves is______ ．
- 16. As we all know, the meaning of | 4 | = | 4-0 |, on the number axis, is the distance between the point of 4 and the origin (that is, the origin of 0). For another example, the meaning of formula | 8-3 |, on the number axis, is the distance between the point of 8 and the point of 3. Similarly, the meaning of formula | a + 5 | on the number axis is________ . If the answer is "the distance between a point and 5 or - 5", please explain the reason in detail!
- 17. If point a represents 7, and now a moves 6 unit lengths along the number axis to point B, then the rational number represented by point B is
- 18. If the distance between the corresponding point of a number on the number axis and its opposite number on the number axis is 5 unit length, then the number is______ Or______ ．
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