Understanding of numbers within 1 100 million;
One hundred thousand:100000;
One million:100000;
Ten million:100000;
1 100 million:1010 million;
2. Several levels
Numeric grading is a way of reading Arabic numerals for people to remember. On the basis of numerical system (numerical order), read and write numbers according to the principle of three-digit or four-digit grading. Usually, in the writing of Arabic numerals, decimal points or spaces are used as the marks of each number level, and the numbers are separated from right to left.
3. Several levels of classification
(1) four-digit classification method
That is, a four-digit grading method. The habit of reading in our country is like this.
Such as: ten thousand (four zeros after counting), one hundred million (eight zeros after counting), and one trillion (12 zeros after counting, which is a normal number). ...
These levels are called Level 1, Level 10,000 and Level 100 million respectively. ...
(2) Three-digit classification
That is, the three-digit grading method. This western classification, this classification is also an internationally accepted classification. For example, thousands, followed by three zeros and millions, six zeros and one billion, and nine zeros.
4. Numbers
Numbers mean that when writing numbers, the numbers are arranged side by side in a line, and each number occupies a position. These positions are called numbers. Starting from the right end, the first place is the unit, the second place is the tenth place, the third place is the hundred places, the fourth place is the thousand places, and the fifth place is the ten thousand places, and so on. This shows that the concept of counting unit and number is different.
5. Generation of numbers
The origin of Arabic numerals: After the ancient Indians created Arabic numerals, they spread to the Arab region around the 7th century. By the 3rd century A.D./KLOC-0, the Italian mathematician Fibonacci wrote Abacus, in which he introduced Arabic numerals in detail. Later, these figures spread from the Arab region to Europe. Europeans only know that these numbers are imported from the Arab region, so they are called Arabic numbers. Later, these figures spread from Europe to all countries in the world.
Arabic numerals were introduced into China around 13 ~ 14 century. Because in ancient China, there was a number called "chip", which was convenient to write. At that time, Arabic numerals were not widely used in China. At the beginning of this century, with the absorption and introduction of foreign mathematical achievements by China, Arabic numerals began to be used slowly in China, and only now have they been popularized and used in China for more than 100 years. Arabic numerals have now become the most commonly used numbers in people's study, life and communication.
6. Natural numbers
A number used to measure the number of things or to indicate the order of things.
That is, the numbers represented by the numbers 0, 1, 2, 3, 4, and ... the numbers representing the number of objects are called natural numbers, and they form an infinite group one by one from 0 (inclusive).
7. Calculation tools
Abacus, calculator, computer
8. Light
In geometry, a figure consisting of a point on a straight line and its edges is called a ray. As shown in the figure below:
Light characteristics
(1) ray has only one endpoint, and it extends from one endpoint to the other indefinitely.
(2) Ray is unpredictable.
9. Straight line
A straight line is the trajectory of a point moving in the same or opposite direction in space.
10. Line segment
A line segment is represented by letters or lowercase letters representing its two endpoints. Sometimes these letters also represent the length of a line segment, which is recorded as line segment AB or line segment BA and line segment A .. where AB represents any two points on a straight line.
1 1. Line segment characteristics
(1) finite length, which can be measured.
(2) Two endpoints
12. Line segment properties
(1) The line segment between two points is the shortest.
(2) The length of the line segment connecting two points is called the distance between these two points.
(3) Two points on a straight line and the part between them are called line segments, and these two points are called the endpoints of the line segments.
There is no distance in a straight line. Ray has no distance. Because a straight line has no end point, and a ray has only one end point, it can extend indefinitely.
13. Coke
Static definition of (1) angle
A figure composed of two non-coincident rays with a common endpoint is called an angle. This common endpoint is called the vertex of the angle, and these two rays are called the two sides of the angle.
(2) Dynamic definition of angle
The figure formed by the rotation of light from one position to another around its endpoint is called an angle. The endpoint of the rotated ray is called the vertex of the angle, the ray at the starting position is called the starting edge of the angle, and the ray at the ending position is called the ending edge of the angle.
14. Angle symbol
Angle symbol:
15. Type of horn
The size of the angle has nothing to do with the length of the side; The size of an angle depends on the degree to which both sides of the angle are open. The bigger the opening, the bigger the angle. Conversely, the smaller the opening, the smaller the angle. In dynamic definition, it depends on the direction and angle of rotation. Angles can be divided into acute angle, right angle, obtuse angle, right angle, rounded corner, negative angle, positive angle, upper angle, lower angle and 0 angle, which are 10 respectively. An angle measuring system in degrees, minutes and seconds is called an angle system. In addition, there are secret system, arc system and so on.
(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) Oblique angle: An angle greater than 90 and less than180 is called obtuse angle.
16. Increase
Multiplication refers to how many times a number or quantity has been increased. For example, 4 times 5, that is, 4 increases 5 times, or it can be said that 5 4' s are added together.
17. Number names in the multiplication formula
"×" is a multiplication sign, the numbers before and after the multiplication sign are called factors, "=" is an equal sign, and the numbers after the equal sign are called products.
10 (factor) × (symbol) 200 (factor) = (symbol) 2000 (product)
18. Parallel
When there is no common point between two straight lines on a plane, two planes in space or a straight line in space and a plane, they are said to be parallel. As shown in the figure, the straight line AB is parallel to the straight line CD and marked as AB∑CD. Parallel lines will never intersect.
19. perpendicular to each other
Two vertical lines, two planes intersect, or a straight line intersects a plane. If the intersecting angles are at right angles, they are said to be perpendicular to each other.
20. parallelogram
Two groups of quadrangles with parallel opposite sides on the same plane are called parallelograms.
2 1. trapezoid
Trapezoid refers to a set of quadrilaterals whose opposite sides are parallel and the other set of opposite sides are not parallel. Two parallel sides are called the bottom of the trapezoid, in which the long side is called the bottom and the short side is called the bottom; You can also simply think that the upper part is called the upper bottom and the lower part is called the lower bottom. Non-parallel edges are called waist; The vertical section sandwiched between the two base sides is called the height of the trapezoid.
22. Separate
Law of division: How many digits is the divisor? Look at the first few digits of the divisor first. If the first few digits are not divided enough, look at one more digit. Except for the one to which it belongs, all the vendors will write on it. It is not enough for quotient one and quotient zero to occupy one position.
The remainder is less than the divisor. If the quotient is decimal, the decimal point of the quotient should be aligned with that of the dividend. If the divisor is a decimal, it must be divided into integers and then calculated.
Extended data
1 1. Numbers, digits and counting units are concepts with different meanings.
"Number" refers to the position occupied by each digit of a number. From the right, the first digit in the numerical sequence table is "unit", the second digit is "ten digits", the third digit is "hundred digits", the fourth digit is "thousand digits", the fifth digit is "ten thousand digits", and so on. The same number represents different values because of different digits. For example, if Arabic numerals are used to represent numbers, the same' 6' in the tenth place is six tens, in the hundredth place is six hundred, in the hundredth place is six hundred, and in the hundredth place is six hundred million.
"Number of digits" refers to the number of digits contained in natural numbers. Numbers like 458 are composed of three numbers, each of which occupies one place, so we call it three digits. 198023456 consists of nine digits, so it is nine digits. "Numbers" and "digits" cannot be confused.
Counting units: one, ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million, one hundred million, one billion, ten billion, one hundred billion ... are all counting units. The counting unit on the unit is one, ten, hundred, thousand, ten thousand, and so on. So when reading, read the numbers first, and then read the counting unit.
22. Knowledge expansion of natural numbers
There are addition and multiplication operations in the set of natural numbers. The result of addition or multiplication of two natural numbers is still a natural number, and subtraction or division can also be done, but the result of subtraction and division is not necessarily a natural number, so subtraction and division operations are not always effective in the set of natural numbers.
Natural numbers are the most basic of all numbers that people know. In order to make the number system have a strict logical basis, mathematicians in the19th century established two equivalent theories of natural numbers: ordinal number theory and cardinal number theory, which made the concept, operation and related properties of natural numbers strictly discussed. Must be an integer. A number used to measure the number of things or to indicate the order of things. That is, the numbers represented by the numbers 0, 1, 2, 3, 4, and ... the numbers representing the number of objects are called natural numbers, and they form an infinite group one by one from 0 (inclusive).
33. Other classifications of angles
Boxer: An angle equal to 180 is called a boxer.
Excellent angle: more than180 and less than 360 is called excellent angle.
Bad angle: more than 0 and less than 180 is called bad angle, and acute angle, right angle and obtuse angle are all bad angles.
Fillet: An angle equal to 360 is called a fillet.
Negative angle: the angle formed by clockwise rotation is called negative angle.
Positive angle: the angle of counterclockwise rotation is positive angle.
Angle 0: An angle equal to zero.
Complementary angle and complementary angle: if the sum of two angles is 90, it is complementary angle; if the sum of two angles is180, it is complementary angle. The complementary angles of equal angles are equal, and the complementary angles of equal angles are equal.
Inverse vertex angle: When two straight lines intersect, there is only one common vertex, and both sides of the two corners are opposite extension lines. These two angles are called antipodal angles. Two straight lines intersect to form two pairs of vertex angles. The two opposite angles are equal.
There are also a variety of angle relationships, such as internal dislocation angle, congruent angle and internal angle of the same side (in the three-line octagon, it is mainly used to judge parallelism).
44. The nature of parallel lines
(1) Two straight lines are parallel and complementary.
(2) The two straight lines are parallel and the internal dislocation angles are equal.
(3) Two straight lines are parallel, and the included angle is equal.
55. Determination of parallel lines (on the same plane)
(1) The internal angles on the same side are complementary, and the two straight lines are parallel.
(2) The internal dislocation angles are equal and the two straight lines are parallel.
(3) The isosceles angles are equal and the two straight lines are parallel.
(4) If two straight lines are parallel to the third straight line at the same time, the two straight lines are parallel to each other.
(5) If two straight lines are perpendicular to the third straight line at the same time, the two straight lines are parallel to each other.
66. Vertical nature
(1) In the same plane, there is one and only one straight line perpendicular to the known straight line.
(2) Of all the line segments connecting a point outside the straight line and a point on the straight line, the vertical line segment is the shortest. Simply put: the vertical line segment is the shortest.
(3) Distance from point to straight line: The length from a point outside the straight line to the vertical section of this straight line is called the distance from point to straight line.