A summary of the rational number mind map of the first volume of mathematics in seventh grade
Mathematical proof of rational number
definition
Rational number boundary
According to the definition, infinite cyclic decimals and finite decimals (integers can be considered as decimals with 0 after decimal point) are collectively called rational numbers, and infinite cyclic decimals are irrational numbers.
However, it is impossible for human beings to write rational numbers with the largest number of digits. It is a rational number for all human beings on the earth, or for creatures smarter than the earth. For everyone on the earth, it may be impossible to know whether it is rational or irrational. Therefore, the boundary between rational numbers and irrational numbers is actually close to irrational numbers, and between any two very close irrational numbers, infinite rational numbers can be added, and vice versa.
No one knows the boundary of rational number, or the boundary of rational number is infinitely close to irrational number.
theorem
Theorem: It is impossible to write a non-infinite cyclic rational number with the largest number of digits. Although its definition has a limited number of digits, it is infinitely close to irrational numbers, so that there is no way to judge.
certificate
Proof: Suppose we write a non-infinite circular rational number with the largest number of digits, and we add one more bit at the end of this number. This number is still a finite rational number, but it is one more than the written rational number, which proves that the original written non-infinite circular rational number is not the largest number. So it is impossible to write a non-infinite cyclic rational number with the largest number of digits.
The seventh grade mathematical rational number exercises.
1, (6 points) Fill in the following numbers in the corresponding set:
-23,0.25, ,-5. 18, 18,-38, 10,+7,0,+ 12
Positive number set: {? }
Integer set: {? }
Music score setting: {? }
2. A proofreader conducted a push-up test on a seventh-grade boy, with seven as the standard, and the number of times exceeded was positive and the number of times insufficient was negative. The scores of eight boys are as follows:
2 - 1 0 3 -2 -3 1 0
(1) What is the percentage of eight boys who meet the standard?
(2) How many push-ups did the eight boys do?
answer
1、
A set of positive numbers: {0.25, 18, 10, +7,+12? }
Integer sets: {-23, 18, -38, 10, +7, 0,+12? }
Score set: {0.25, -5. 18? }
2、
( 1)50%, (2)56
Seventh grade mathematical rational number mind map Volume I related articles:
1. Handwritten newspaper with pictures of mathematical rational numbers.
2. The first volume of the seventh grade mathematics handwritten newspaper
3. The contents of the first volume of the seventh grade mathematics handwritten newspaper
4. The seventh grade mathematical mind map
5. Math Mind Map of Grade One.
6. The first chapter of the mathematical mind map.