Integer number sequence table
Several levels, hundreds of millions, ten thousand levels, personal level.
Hundreds of billions, billions, billions, tens of millions, hundreds of thousands, hundreds of thousands, tens of thousands.
Counting units ... 1000 billion, 1000 billion, 1 billion, 11.
1. The advance rate between every two adjacent counting units is 10. This counting method is called decimal counting method.
Look at the table: for example, 1 010 million means10 million, and10 million means10 million.
Number of digits: unit, ten, hundred, thousand, ten thousand, one hundred thousand, one million, ten million, one billion, one billion …
Counting unit: unit, ten, hundred, thousand, ten thousand, one hundred thousand, one million, ten million, one billion …
How many "ones" are represented by series. How many tens of thousands of numbers represent tens of thousands. How many "billions" do billions of numbers represent?
Every four digits are one level. Divided into: grade, grade, grade.
Reading: Start from a high position, read the numbers of 100 million or 10,000 levels step by step according to the reading method of 100 million, and then add a word "100 million" or "10,000" after it. There is a zero in the middle of the number or several consecutive zeros, all of which are read only, and the zeros at the end of each level are not read.
Write number: write 100 million first, then 10 thousand, and finally write one. Whoever doesn't have the previous unit will write 0 as a placeholder.
3.308 4000 0860 consists of three tens, eight hundred, four tens, eight hundred and six tens; It can also be said that it is composed of 30.8 billion yuan, 40 million yuan and 860 yuan.
4. "Rounding" method: 4, 3, 2, 1, 0 is rounded; 5, 6, 7, 8, 9 are discarded and moved forward to 1.
5. The difference between "=" and "material":
7580000 = 75808000 ≈ 75 10000
90000000000 = 9 billion 9420000000 ≈ 9.4 billion
Omission and rewriting: 958 5006 5200
When the mantissa after 1 100 million bits is omitted, it depends on1100 million bits: 959 0000 0000.
Rewrite the number in "100 million" to: 95.9 billion.
6. Compare the sizes of numbers
The number of digits is different, and the number of digits is large; If the number of digits is the same, the largest number from the left is larger. If the first number from the left is the same, compare the second number from the left. ...
7. Numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,1,... are all natural numbers.
There is no object, which is represented by 0. 0 is also a natural number.
The smallest natural number is 0. There is no maximum natural number, and the number of natural numbers is infinite.
0 cannot be partitioned. For example, 5÷0 cannot get the quotient, because no number can be multiplied by 0 to get 5.
Another example: 0÷0 can't get the quotient, because any number multiplied by 0 gets 0.
8. In multiplication, one factor is a constant, another factor is divided by several times or multiples, and the product is also divided by several times or multiples.
In division, the dividend and divisor are expanded or reduced by the same multiple (except 0) at the same time, and the quotient remains unchanged.
In division, the divisor remains the same, the dividend becomes larger and the quotient becomes larger.
In division, the divisor is constant, the divisor becomes larger and the quotient becomes smaller.
180÷30: It can be regarded as 180 divided by 30 or 30 divided by 180.
The estimation of two-digit division is generally to regard two digits as an integer close to it, and then calculate the result orally.
In pen division, the divisor is regarded as an integer ten. If the product is less than and closest to the divisor, the quotient or trial quotient is used.
Starting from the high digits of dividend, look at the first two digits of dividend; If the first two digits are less than the divisor, it depends on the first three digits; In addition to the dividend, the business is written on that one; The remainder must be less than the divisor.
Two-digit multiplication: first multiply the number on one multiplier by another multiplier, and the end of the number is aligned with the number; Multiply the number in the tenth place of this multiplier by another multiplier, and the end of the number is aligned with the tenth place. Finally, add the products of the two multiplications.
Multiply the number before 0 first, then see how many zeros are at the end of the multiplier * * *, and fill in a few zeros at the end of the multiplied number.
Second, space and graphics.
The 1. line segment has two endpoints, and the length can be measured.
A ray has only one endpoint and can extend to one end indefinitely. You can draw countless rays from a point.
A straight line has no end points and can extend to both ends indefinitely. You can draw countless straight lines through any point, and only one straight line can be drawn through any two points.
2. A figure consisting of two rays from a point is called an angle. This point is called the vertex of the angle, and these two rays are called the edges of the angle. The sign of the angle is "∞".
To measure the angle, use a protractor. The unit of measurement of an angle is "degree". Indicated by the symbol "0".
The size of an angle has nothing to do with the length drawn on both sides of the angle, but depends on the size of both sides.
Acute angle: less than 90; Right angle: equal to 90; Oblique angle: greater than 90 and less than 180.
Flat angle: equal to 180 fillet: equal to 360 1 flat angle =2 right angle 1 fillet =2 flat angle =4 right angle.
The clock is 30 per hour, for example, the angle between two hours is 60.
The sum of internal angles of triangle is 180, and the sum of internal angles of quadrilateral is 360.
∠ 1 and ∠2 are on the same side of the same line, that is, the two angles form a right angle, ∠ 1+2 = 180.
3. Two straight lines that do not intersect in the same plane are called parallel lines, or they are parallel to each other.
If two lines intersect at right angles, they are said to be perpendicular to each other, one of which is called the perpendicular of the other, and the intersection of these two lines is called the vertical foot.
The vertical line segment drawn from a point outside the straight line is the shortest, and its length is called the distance from that point to the straight line.
5. The distance between parallel lines is equal everywhere.
6. Two groups of parallelograms with parallel opposite sides are called parallelograms. Parallelogram is easy to deform.
Rectangular and square can be regarded as special parallelograms.
A quadrilateral with only one set of parallel sides is called a trapezoid. An isosceles trapezoid is called an isosceles trapezoid.
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. Draw a high line with a dotted line to mark the foot.
Two identical trapezoids can be combined into a parallelogram.
Two parallelograms with the same height are still parallelograms.
7. Relationship diagram between quadrangles.
8. Parallelogram: two groups of opposite sides are parallel respectively; The two groups of opposite sides are equal respectively.
Rectangular: two groups of opposite sides are parallel respectively; The two groups of opposite sides are equal respectively; There are four right angles.
Square: two groups of opposite sides are parallel respectively; The two groups of opposite sides are equal respectively; Four sides are equal, four right angles.
A rectangle has two symmetry axes, a square has four symmetry axes, and an isosceles trapezoid has only 1 symmetry axis.
Third, the relationship between memory quantity
Speed x time = distance unit price x quantity = total price
Work efficiency × working hours = total workload.
Distance/Time = Total Speed/Quantity = Unit Price
For example: speed 80km/h: speed 80km/h: speed 240km/h: 3 o'clock, 8 copies of each 5 yuan: 5 yuan/Ben 40 yuan.
225m per minute: 225m/min 1800m 8 minutes; each 28 yuan: 28 yuan/Zhang 168 yuan, 6.
The first unit division
1, divisor is a written calculation rule for dividing two digits:
(1) Look at the first two digits of the dividend from its high digits;
(2) If the first two digits are less than the divisor, it depends on the first three digits; In addition to the dividend, the business is written on that one;
(3) The remainder 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. It should be reduced when the trial quotient is large, and increased when the trial quotient is small.
3. In the division formula with remainder, dividend = quotient divisor+remainder.
4. When three digits are divided by two digits, the quotient may be one digit or two digits.
Second unit angle
1. Extend one end of the line indefinitely and you will get a ray. Extend both ends of the line indefinitely and you will get a straight line. Line segments and rays are both parts of a straight line.
Similarities and differences of graphics
Line segments are all straight lines with two endpoints, and the length is limited (measurable).
A ray has an endpoint, which is infinite.
A straight line has no end points and is infinitely long.
2. You can draw countless straight lines after one o'clock, and only one straight line after two o'clock (two points determine a straight line).
3. In the connection between two points, the line segment is the shortest.
The length of the line segment connecting two points is called the distance between these two points.
Draw two rays from a point to form an angle. The angle is usually represented by the symbol "∞".
5. A corner has a vertex and two sides.
6. The size of the angle is related to the size of both sides, not to the length of the sides.
7. A protractor is a tool for measuring angles. Divide the semicircle into 180 equal parts (divided into 180 parts on average), and the angle of each part is 1 degree. "Degree" is the unit for measuring angles, which is represented by the symbol "0". For example, 1 is recorded as 1.
8. Angle measurement and angle drawing should be "point to point, line to the opposite side, and then look at the other side. 0 is inside the internal number and 0 is outside the external number.
9. The acute angle is less than 90; A right angle equals 90 degrees; Obtuse angle greater than 90 and less than180; Boxer180; Fillet 360.
1 fillet =2 right angle =4 right angle.
10, 1 hour, clockwise turns a big grid, diagonal 30; When the minute hand turns once, the right angle is 360.
Unit 3 Mixing Operation
1, in the mixed operation without brackets, if it only contains addition, subtraction or multiplication and division, it should be calculated from left to right; If you count addition, subtraction, multiplication and division, first calculate multiplication and division, then add and subtract.
2. In the mixed operation using parentheses, the inner side of parentheses should be calculated first.
Unit 4 Parallelism and Intersection
1. On the same plane, two disjoint straight lines are parallel to each other, one of which is parallel to the other. (In the same plane, two straight lines intersect if they are not parallel)
2. When drawing parallel lines, first put a triangular ruler, then put a ruler and translate the triangular ruler.
When two straight lines intersect at right angles, they are perpendicular to each other, and one of them is perpendicular to the other. The intersection of these two straight lines is called vertical foot.
4. When drawing a vertical line, put a ruler first, then a triangular ruler, and translate the triangular ruler.
5. The vertical line segment between a point and a straight line is the shortest.
The length of a vertical line segment drawn from a point outside a straight line is called the distance from that point to this straight line.
6. All vertical line segments between two parallel lines are equal in length.