1. Recognition of large numbers
Recognition of numbers up to one hundred million:
100,000: 10 ten thousand;
One million: 10 hundred thousand;
10 million: 10 million;
100 million: 10 one million;
100 million: 10 ten million;
2. Number level
Number level is to facilitate people to remember to read the Arabic number of a literacy method, in the place value system (the order of the digits) based on the principle of three- or four-digit grading, the number of readings, written out. Usually in the writing of Arabic numbers, the decimal point or space as the identification of each level, from right to left to separate the number.
3. Classification
(1) four-digit classification
That is, the four-digit number for a number of classification methods. The habit of reading in our country is to read according to this method.
Such as: ten thousand (four zeros after the number), billion (eight zeros after the number), trillion (twelve zeros after the number, which is counted in the middle method) ......
These levels are called a level, ten thousand level, billion level ......
(2) Three-digit grading method
That is, the three-digit number as a number of grades of the grading method. This Western grading method, this grading method is also the internationally recognized grading method. For example: thousand, three 0s after the number, million, six 0s after the number, billion, nine 0s after the number .......
4. Digits
A digit is a number that is written side by side in a horizontal row, with one digit occupying one position, and these positions are called digits. Counting from the right, the first digit is the "digit", the second is the "tens digit", the third is the "hundreds digit", the fourth is the "thousands digit", and the fifth is the "thousands digit". "and the fifth digit is "ten thousand", etc. This shows that the unit of counting and the number of digits are the same. This shows that the concepts of counting units and digits are different.
5. The Creation of Numbers
Origin of Arabic Numerals: After the ancient Indians created Arabic numerals, they spread to the Arab region around the 7th century AD. By the 13th century, the Italian mathematician Fibonacci wrote the Book of Abacus, in which he gave a detailed description of Arabic numerals. Later, these numbers were again transmitted from the Arab region to Europe. The Europeans only knew that these numbers were imported from the Arab region, so they called these numbers Arabic numerals. Later on, these numbers were spread from Europe to countries all over the world.
Arabic numerals were introduced to our country around the 13th to 14th century. Because there is a kind of numbers called "chips" in our ancient times, it is easier to write, so the Arabic numerals were not popularized and used in our country in a timely manner. At the beginning of this century, with the absorption and introduction of foreign mathematical achievements, Arabic numerals began to be used slowly in our country, and the popularization of Arabic numerals in our country has a history of more than 100 years. Arabic numerals have now become the most commonly used numbers in people's studies, lives and interactions.
6. Natural numbers
Used to measure the number of things or the number of things in order.
That is, the numbers represented by the digits 0, 1, 2, 3, 4, ....... The number that represents the number of objects is called the natural number, and the natural numbers start from 0 (including 0), one after the other, forming an infinite collective.
7. Calculating tools
Abacus, calculator, computer
8. Rays
In geometry, the figure formed by a point on a straight line and the portion of the line that is next to it is called a ray. It is shown in the figure below:
Characteristics of rays
(1) A ray has only one endpoint, and it extends indefinitely from one endpoint to the other.
(2) Rays are not measurable.
9. A straight line
A straight line is a trajectory of points moving in the same or opposite direction in space.
10.Line Segment
A line segment is represented by a letter denoting its two endpoints or by a lowercase letter, sometimes these letters also denote the length of the line segment, notated as line segment AB or line segment BA, line segment a. Where AB denotes any two points on the line.
11. Characteristics of line segments
(1) finite length, can be measured
(2) two endpoints
12.
(2) The length of the line segment connecting two points is called the distance between these two points.
(3) Two points on a line and the portion between them are called the segment, and these two points are called the endpoints of the segment.
A straight line has no distance. Rays also have no distance. Because, while a straight line has no endpoints, a ray has only one endpoint and can be extended indefinitely.
13. Angle
(1) Static Definition of Angle
The figure formed by two non-overlapping rays having a common **** endpoint is called an angle. This common *** endpoint is called the vertex of the angle and the two rays are called the two sides of the angle.
(2) Dynamic Definition of Angle
The figure formed by rotating a ray around its endpoint from one position to another is called an angle. The endpoint of the rotated ray is called the vertex of the angle, the ray at the start position is called the beginning edge of the angle, and the ray at the end position is called the end edge of the angle
14. The size of an angle has nothing to do with the length of the sides; it is determined by how far the two sides of the angle are spread; the greater the spread, the larger the angle, and conversely, the smaller the spread, the smaller the angle. In the dynamic definition, it depends on the direction and angle of rotation. Angles can be categorized into 10 types: acute, right, obtuse, flat, circumferential, negative, positive, superior, inferior, and zero. The measurement system of angles in degrees, minutes and seconds is called the angle system. In addition, there is a dense bit system, radian system, etc..
(1) acute angle: an angle greater than 0° and less than 90° is called an acute angle.
(2) Right Angle: An angle equal to 90° is called a right angle.
(3) Obtuse Angle: An angle greater than 90° and less than 180° is called an obtuse angle.
16.Multiplication
Multiplication is a number or quantity, increased by how many times. For example, if you multiply 4 by 5, it means that 4 is increased by a factor of 5. It can also be said that 5 4s are added in a row.
17. The names of the numbers in a multiplication equation
"x" is the multiplication sign, and the numbers in front of and behind the multiplication sign are called the factors, and "=" is the equal sign, and the numbers behind the equal sign are called the product.
10 (factors) × (multiplication sign) 200 (factors) = (equal sign) 2000 (product)
18. Parallel
When there is no common **** point between two straight lines in a plane, two planes in space, or a line in space and a plane, they are said to be parallel. As shown in the figure the line AB is parallel to the line CD, denoted as AB∥CD. parallel lines never intersect.
19. Mutually perpendicular
Perpendicular to two straight lines, two planes intersect, or a straight line and a plane intersect, if the angle of intersection at right angles, called mutually perpendicular.
20.Parallelogram
A quadrilateral with two sets of opposite sides parallel to each other in the same plane is called a parallelogram.
21.Trapezium
A trapezium is a quadrilateral in which one set of opposite sides are parallel and the other set of opposite sides are not. The parallel sides are called the base of the trapezoid, of which the long side is called the bottom and the short side the top; or you can simply think of the top one as the top and the bottom one as the bottom. The two sides that are not parallel are called the waist; the vertical segment sandwiched between the two bottoms is called the height of the trapezoid.
22.
The remainder should be smaller than the divisor, and if the quotient is a decimal, the decimal point of the quotient should be aligned with the decimal point of the divisor; if the divisor is a decimal, it should be converted into a whole-number division and then calculated.
Extended information
11. "Number of digits" and "digit" and "unit of counting" are concepts with different meanings.
A "digit" is the place occupied by each digit of a number. The list of digits from the right end, the first is "digit", the second is "tens", the third is "hundreds", the fourth is "thousands", the fifth is "thousands", the fourth is "thousands", the fourth is "thousands", the fourth is "thousands", the fourth is "thousands", and the fifth is "thousands". "The fifth digit is "ten thousand", etc. The same number, because of the number of digits in which it is located, is not the same as the number of digits in which it is located. The same number, due to the location of the different digits, it represents a different value. For example, in the use of Arabic numerals to indicate the number, the same '6', placed in the ten position to indicate six tens, placed in the hundreds position to indicate six hundreds, placed in the billions position to indicate six billions, and so on.
"Digits" refers to the number of digits in a natural number. The number 458 has three digits, and each digit occupies one digit, so we call it a three-digit number. 198023456 consists of nine digits, so it is a nine-digit number. The term "digit" is not to be confused with "digit".
Counting units: one (one), ten, one hundred, one thousand, one hundred thousand, one hundred thousand, one million, ten million, one hundred million, one hundred million, one billion, ten billion, one hundred billion ...... are all counting units. The unit of count in the "digit" is "one", the unit of count in the "tens" is "tens", the unit of count in the "hundreds" is "one", the unit of count in the "hundreds" is "ten", and the unit of count in the "hundreds" is "one". The unit of count in the hundreds place is the hundred, the unit of count in the thousands place is the thousand, and the unit of count in the tens place is the ten thousand. The unit of count in the "thousand" is "thousand", the unit of count in the "ten thousand" is "ten thousand", and so on. So when you read a number, you read the number first and then the unit of count.
22. Extension of knowledge of natural numbers
The set of natural numbers has the operations of addition and multiplication, the result of adding or multiplying two natural numbers is still a natural number, and can be subtracted or divided, but the result of the subtraction and division may not always be a natural number, so subtraction and division operations in the set of natural numbers is not always possible.
The natural numbers are the most fundamental class of all numbers recognized by people. In order to give the system of numbers a rigorous logical foundation, 19th-century mathematicians established two equivalent theories of the natural numbers: the theory of the ordinal numbers and the theory of the base of the natural numbers, which led to a rigorous exposition of the concepts, operations, and related properties of the natural numbers. Must be an integer. A number used to measure the number of pieces of something or to indicate the order of things. That is, a number represented by the digits 0, 1, 2, 3, 4, ....... The number that indicates the number of objects is called a natural number, and natural numbers start from 0 (including 0), one after the other, forming an infinite collective.
33. Other Classifications of Angles
Flat Angles: an angle equal to 180° is called a flat angle.
Superior angles: angles greater than 180° and less than 360° are called superior angles.
Inferior angles: angles greater than 0° and less than 180° are called inferior angles; acute, right, and obtuse angles are all inferior angles.
Circumferential angle: an angle equal to 360° is called a circumferential angle.
Negative angle: An angle made by rotating in clockwise direction is called negative angle.
Positive angle: an angle rotated counterclockwise is a positive angle.
0 angle: an angle equal to zero degrees.
Remainder and Complementary Angles: Two angles whose sum is 90° are considered as remainders of each other, and two angles whose sum is 180° are considered as complements of each other. Equal angles have equal remainder angles and equal complementary angles.
Diagonal angle: two straight lines intersecting the resulting only a common **** vertex and the two sides of the two angles to each other for the reverse extension, so the two angles are called each other for the diagonal angle. Two straight lines intersect, forming two pairs of opposite angles. Two angles that are opposite to each other are equal.
There are also many kinds of angle relationships, such as interior angles, congruent angles, congruent interior angles (three lines and eight angles, mainly used to determine parallel)
44.
(2) Two lines are parallel and the interior angles are equal.
(3) Two lines are parallel and congruent angles are equal.
55. Determination of Parallel Lines (in the same plane)
(1) Same-side interior angles are complementary and two lines are parallel.
(2) Interior angles are equal and two lines are parallel.
(3) Identical angles are equal and two lines are parallel.
(4) Two lines are parallel to each other if they are simultaneously parallel to a third line.
(5) If two lines are simultaneously perpendicular to a third line, then these two lines are parallel to each other.
66. Properties of a Perpendicular
(1) In the same plane, there is one and only one line perpendicular to a known line through a point.
(2) Of all the segments connecting a point outside a line to points on the line, the vertical segment is the shortest. Simply put: the vertical line segment is the shortest.
(3) Distance from the point to the line: the length of the segment from the point outside the line to the line is called the distance from the point to the line.