1, 10 is ten thousand, 10 is one hundred thousand, 10 is one million, 10 is one million.

2 2. 10/010 million is one hundred million,1010 billion is one billion,1010 billion is ten billion,10100 billion is one hundred billion.

3. One, ten, one hundred, ten thousand, one hundred thousand, one million, ten million, one hundred million, one billion ... are all counting units.

According to our country's counting habit, starting from the right, every four digits are one level.

Numeric sequence table

How many levels ... 100 million, 10 thousand.

Numbers ... billions, billions, billions, hundreds, thousands, hundreds, dozens.

Counting unit ... 100 billion billion billion billion billion.

5. The counting method with the ratio of 10 between every two adjacent counting units is called decimal counting method.

6. Reading, just add "10,000" or "100 million" at the end of each level; The zero at the end of each level is not read, and other numbers have one or several zeros, and all of them read only one "zero".

7. When writing numbers, 10,000-and 100-million-level numbers are written according to the method of first-level numbers. If any number is not enough, 0 will be added. To rewrite numbers in units of "10,000" or "100 million", just remove the four zeros or eight zeros at the end, or add the words "10,000" or "100 million". Rewrite this multi-digit number as "10,000". 38600 . 8886868886 1

8. Usually, we use rounding method to approximate a number by omitting the mantissa.

The method is: look at the number in the highest digit of mantissa, if it is 4 or less, discard mantissa and add a counting unit "10000" or "1 100 million" at the end of the number; If it is 5 or more, add 1 to the previous digit, then discard the mantissa and add the counting unit "10000" or "1000000". Get a rough figure, with a ""in the middle.

9.1,2, 3, 4, 5, 6, 7, 8, 9,10,1,... representing the number of objects are all natural numbers. An object is not represented by 0, and 0 is also a natural number. The smallest natural number is 0, and there is no maximum.

10. The computing tool invented by China in14th century and still used today is abacus. A bead above the abacus represents 5, and a bead below the abacus represents 1.

1 1. On the calculator, the ON/C key is the switch and the screen clear key, the CE key is the clear key, and the AC key is the reset key. The+,-,× and \ keys are operation symbol keys.

Measurement of the second unit angle

1. A straight line has no endpoints and can extend to both ends indefinitely, so its length cannot be measured.

2. Ray has an endpoint, which can extend to one end indefinitely, and its length cannot be measured.

3. A line segment has two endpoints, and its length can be measured.

4. Infinitely extend one end of the line segment to obtain rays. Extend both ends of the line segment infinitely to get a straight line. Line segments and rays are both parts of a straight line.

You can draw countless straight lines and rays after one o'clock. You can only draw a straight line after two o'clock.

6. The figure formed by two rays from a point is called an angle. This point is the vertex of an angle, and these two rays are the sides of an angle. An angle is usually represented by a symbol ("∞").

7. The size of the angle has nothing to do with the length drawn on both sides of the angle. The size of the angle depends on the size of both sides of the angle. The bigger the sides of the angle, the bigger the angle.

8. The measurement unit of angle is "degree", which is indicated by the symbol "".

9. The protractor divides the semicircle into 180 equal parts, and the angle of each part is 1 degree, which is recorded as "1 degree".

10, diagonally equal.

1 1, the sum of three angles of a triangle is 180 degrees, and the sum of four angles of a quadrilateral is 360 degrees.

12, right angle equals 90 degrees, right angle equals 180 degrees, and fillet equals 360 degrees.

13, 1 flat angle =2 right angles. 1 fillet = 2 straight angle = 4 right angle.

14, acute angle less than 90 degrees, obtuse angle more than 90 degrees less than 180 degrees;

15, acute angle 16, turn a large grid clockwise, diagonal 30; When the minute hand turns once, the right angle is 360.

Unit 3 Multiply three numbers by two numbers

1. When multiplying three digits by two digits, first multiply three digits by two digits, and then multiply three digits by ten digits of two digits. Finally, add up their products.

2. Multiply with 0 at the end of the factor: when writing vertically, align the numbers before 0 and multiply only the numbers before 0; There are several zeros at the end of two factors, and several zeros are added at the end of the product.

3. If one factor remains the same, another factor will expand (or shrink) several times, and the product will also expand (or shrink) by the same multiple.

4. If one factor is expanded or reduced by several times and another factor is expanded or reduced by the same multiple, the product remains unchanged.

For example, one factor is enlarged by 2 times, and the other factor is reduced by 2 times, unchanged.

5. One factor multiplies, another factor multiplies, and the product multiplies. For example, 5×3= 15,

(5×2)×(3×2)= 15×4

6. Speed × time = distance/time = speed/distance/speed = time

Unit price × quantity = total price ÷ total price ÷ quantity = unit price ÷ total price ÷ unit price = quantity

Unit 4 Parallelogram and Trapezoid

1. Two straight lines that do not intersect in the same plane are called parallel lines, or they are parallel to each other.

2. If two straight lines intersect at right angles in the same plane, that is to say, they are perpendicular to each other, and one of them is called the perpendicular of the other, and the intersection of these two straight lines is called the vertical foot.

3. If two straight lines are parallel to the third straight line, then the two straight lines are also (parallel to each other).

If both lines are perpendicular to the third line, then the two lines are also (parallel to each other).

5. The shortest (vertical line segment) drawn from a point outside the straight line is called the (distance) from the point to the straight line. The distance between parallel lines is equal everywhere.

6. Rectangular: the opposite sides are equal, the four corners are right angles, and the two groups of opposite sides are parallel respectively.

7. The circumference of a rectangle = (length+width) × 2; Area of rectangle = length × width;

Square: Four sides are equal, four corners are right angles, and two groups of opposite sides are parallel.

9, the perimeter of the square = side length × 4; Area of a square = side length × side length.

10 Two groups of parallelograms with parallel opposite sides are called parallelograms. Their characteristics are: the opposite side is equal, and the diagonal is equal. Two groups of opposite sides are parallel respectively.

1 1, a quadrilateral with only one set of parallel sides is called a trapezoid. It is characterized in that only one set of parallel edges is parallel and the other set is not parallel. The parallel side is called the bottom of the trapezoid, and the long side is called the bottom; Non-parallel edges are called waist; The distance between the two bases is called the height of the trapezoid.

12, square is a special rectangle; Rectangular and square are special parallelograms.

13, parallelogram is easy to deform and has the characteristics of instability.

14. Draw a vertical line from one point on one side of the parallelogram to the other. The line segment between this point and the vertical foot is called the height of the parallelogram, and the side where the vertical foot is located is called the bottom of the parallelogram.

15, isosceles trapezoid is called isosceles trapezoid. The two base angles of an isosceles trapezoid are equal.

16, two identical trapezoids can be combined into a parallelogram.

17, two identical triangles can be combined into a parallelogram.

Among the figures we studied, rectangle, square, isosceles trapezoid and diamond are symmetrical figures.

19, a point beyond the straight line can only draw a vertical line of a known straight line;

20. When intersecting with points outside a straight line, only parallel lines with known straight lines can be drawn.

2 1、

The divide of unit 5 is that division of two digits.

1. Division calculation rule: the divisor is the division of two digits. First, try to divide the first two digits of the dividend by the divisor. If the first two digits are not enough, try to divide the first three digits of the dividend, and the quotient will go to which place. The remainder of each divisor must be less than the divisor.

Divider is the division of two digits. Generally, the divisor is regarded as an integer close to it to try quotient. When you are trying to get into business, you should drop, and when you are young, you should rise.

3. When three digits are divided by two digits, the quotient may be one digit or two digits.

4. Quotient invariance: In division, the dividend and divisor are multiplied by several (or divided by several) at the same time, and the quotient remains unchanged (except 0).

5. In division, the divisor is constant, the dividend is multiplied (or divided), and the quotient is also multiplied (or divided).

6. In division, the dividend is constant, the divisor is several times (or fractions), but the quotient is several times (or multiples).

7. The relationship of remainder division: dividend ÷ dividend = quotient ... remainder.

Dividend = quotient × divisor+remainder

Unit 6 Statistics

1. The meaning of the bar chart: the bar chart represents a certain amount with unit length, draws straight lines with different lengths according to the amount, and then arranges these straight lines in a certain order. The advantage of a bar chart is that it is easy to see the quantity.

2. Features of bar graph:?

(1) enables people to see the size of each data at a glance.

(2) Differences between data are relatively easy.

3. The statistical charts we have studied include horizontal bar chart, vertical bar chart, simple chart and retest chart.

4. Re-examination statistics are generally composed of numbers, graphics, titles and notes. There are strip statistics, fan statistics, broken line statistics and net statistics in the administrative professional ability test.

Summary of knowledge points in the second volume of mathematics in the fourth grade of primary school in the new curriculum standard textbook of People's Education Press

(1) Four operations:

1, and the operation order is 1. In the formula without brackets, if there is only addition and subtraction or only multiplication and division, it should be calculated from left to right.

2. In the formula without brackets, there are addition, subtraction and multiplication and division, so you should calculate multiplication and division before addition and subtraction.

3. When there are brackets in the formula, count the brackets first.

2. Addition, subtraction, multiplication and division are called four operations.

3. Operate 0: 1, and add 0 to a number to get the original number.

2. Multiply any number by 0 to get 0.

3, 0 can't be divided. 0 divided by a nonzero number equals 0.

0÷0 can't get a fixed quotient; 5÷0 can't get the business.

(2) Location and direction:

1, according to the direction and distance to determine or draw the specific position of the object. (Scale, Angle Drawing and Measurement)

2. Relativity between positions. It will describe the mutual positional relationship between two objects. (Determination of observation points)

3. Draw a simple road map.

(3) Operation method and simple operation:

1, law of addition operation: 1, additive commutative law: two numbers are added, the addend positions are exchanged, and the sum is unchanged.

a+b=b+a

2, the law of addition and association: three numbers are added, you can add the first two numbers first, and then add the third number; Or add the last two numbers first, then add the first number, and the sum remains the same. (a+b)+c=a+(b+c)

These two laws of addition are often used in combination.

For example:165+93+35 = 93+(165+35) What is the basis?

2. The essence of continuous subtraction: one number minus two numbers equals the sum of this number minus those two numbers.

a-b-c=a-(b+c)

3. Multiplication algorithm: 1. Multiplication and exchange law: when two numbers are multiplied, the position of the exchange factor remains unchanged.

a × b = b × a

2. Multiplication and association law: When three numbers are multiplied, you can multiply the first two numbers and then the third number, or you can multiply the last two numbers and then the first number, and the product remains unchanged.

(a × b )× c = a × ( b × c)

These two multiplication laws are often used in combination.

Such as: 125×78×8.

3. Multiplication and distribution law: the sum of two numbers is multiplied by one number. You can multiply these two numbers by these two numbers respectively, and then add up the products. (A+B) × C = A× C+B× C。

4. The nature of continuous division: one number divided by two numbers equals the product of these two numbers.

a ÷ b ÷ c = a ÷ ( b × c)

5. Simple calculation of expansion:

102×38-38×2 125×25×32 125×88 3.25+ 1.98 10.32- 1.98 37×96+37×3+37

Error-prone situation: 0.6+0.4-0.6+0.4 38×99+99.

(4) The meaning and nature of decimals:

Fractions with denominators of 1, 10, 100, 1000 ... can be expressed in decimals.

Decimal is another form of decimal.

3. Decimals are counted in tenths, hundredths and thousandths ... Write 0. 1, 0.0 1, 0.00 1 ...

4. The propulsion rate between every two adjacent counting units is 10.

5. Decimal reading and writing method: reading method: read the integer part according to the integer reading method, and the decimal part should read each number in order.

Writing: the integer part is written as an integer, the integer part is 0, and the decimal part writes each number in turn.

6. Properties of decimals: Add "0" or remove "0" at the end of decimals, and the size of decimals remains unchanged. Note: the "0" in the middle of the decimal cannot be removed, and some "0" at the end cannot be removed when approximating numbers. Functions can simplify decimals, etc.

7. Decimal size comparison: compare the integer part first, the integer part is the same as the decimal part, and the decimal part is the same as the percentile. ...

8. Decimal size change law caused by decimal position movement:

Decimal point to the right: move one place, and the decimal point will be expanded to 10 times the original number;

Move two places, and the decimal will be expanded to 100 times of the original number;

Move three places, and the decimal will be expanded to 1000 times of the original number;

……

Decimal point moves to the left: move one place, and the decimal point is reduced by 10 times (the decimal point is reduced to the original number);

If you move two places, the decimal will be reduced by 100 times.

If you move three digits, the decimal number will be reduced by 1000 times (the decimal number will be reduced to the original number);

……

9. Rewrite the name number: 1 ton, 30kg+800g = () ton.

Unit of length: kilometer —————————————— decimeter ———————— centimeter.

Area unit: square kilometer-hectare-square meter-square decimeter-square centimeter.

Mass unit: ton-kilogram-gram

10, find the approximate number of decimal places (rounding): (Keep the expression with two decimal places, with the accuracy of 1%)

Keep an integer, indicating accuracy to one place, one decimal place, indicating accuracy to ten places, and two decimal places, indicating accuracy to one hundred places. When taking an approximation, the 0 after the decimal point cannot be removed.

Rewrite large numbers. Rewrite first, then find the approximate number. Note: with units.

(5) Triangle:

1. Definition of triangle: A figure surrounded by three line segments (the endpoints of every two adjacent line segments are connected or overlapped) is called a triangle.

Draw a vertical line from the vertex of the triangle to its opposite side. The line segment between the vertex and the vertical foot is called the height of the triangle, and the opposite side is called the bottom of the triangle. Key point: the drawing method of triangle height.

3. Characteristics of triangle: 1. Physical characteristics: stability, such as tripod on bicycle and tripod on telephone pole.

2. Edge features: the sum of any two edges is greater than the third edge.

4, the classification of triangle:

By angle: acute triangle, right triangle, obtuse triangle.

Divided by side length: triangle with unequal sides and isosceles triangle (equilateral triangle or regular triangle is a special isosceles triangle).

The three sides of an equilateral triangle are equal and each angle is 60 degrees.

5. The sum of the internal angles of the triangle is equal to 180 degrees. Calculation and format of degree.

6. Graphic combination: Two identical triangles can be combined into a parallelogram.

7. Dense shop: The patterns that can be densely laid are rectangle, square, triangle and regular hexagon.

(6) Addition and subtraction of decimals:

1, calculation rule: the same digit is aligned (decimal point is aligned), and the calculation is made according to the integer calculation method. The decimal point of the obtained number should be aligned with the decimal point on the horizontal line. The result is that the decimal point should be simplified according to its nature.

2. Vertical calculation and check calculation. Note that the answer should be written in the horizontal direction, not the result of checking calculation.

3. The four operation sequences and algorithms of integers are also applicable to decimals.

(7) Statistics:

Broken line statistical chart: a unit length is used to represent a certain quantity, points are drawn according to this quantity, and then the points are connected in turn by line segments.

Advantages: You can not only see the quantity, but also see the change of quantity, predict the future trend, and provide guidance and help for future production and life.

(8) Mathematical wide angle: planting trees.

Number of intervals = total length ÷ interval length

Situation classification: 1, planting at both ends: number of plants = number of intervals+1.

2. Planting one head and not planting the other: number of plants = number of intervals.

3. No planting at both ends: number of plants = number of intervals-1.

4. Close: number of trees = number of intervals.