1. 10 one thousand is ten thousand, 10 ten thousand is one hundred thousand, 10 one hundred thousand is one million, and 10 one million is ten million.
2. 10 ten million is one hundred million, 10 one hundred million is one billion, 10 one hundred million is ten billion, and 10 one hundred billion is one hundred billion.
3. One (one), ten, one hundred, one million, one hundred thousand, one million, one million, one hundred million, one billion, one billion ...... are all units of counting.
4, according to our counting ** habit, from the right, every four digits is a level.
Number Order Table
Number Level ...... Billion Level 10,000 Level Individual Level
Number Level ...... Thousand Billion Billion Billion Billion Billion Million Million Hundred Thousand Hundred Thousand Hundred Thousand Ten Individual Level
Counting Units ...... thousands of billions of billions of billions of billions of millions of millions of hundreds of thousands of thousands of hundreds of tens
5. The method of counting in which the rate of progression between every two adjacent units of counting is 10 is called decimal counting.
6, when reading, just at the end of each level with "million" or "billion" word; each level of the end of the 0 are not read, the other digits have a 0 or a few 0, are only read a "zero! ".
7, write the number, ten thousand and billion on the level of the number are in accordance with the level of the number of ways to write, which one is not enough to make up with zero. Rewrite "10,000" or "billion" as a unit of number, as long as the end of the 4 0 or 8 0 removed or added "10,000" or "billion" word on the line. 1.1. "1. Rewrite multi-digit numbers as "million" or "billion". In the middle of the "=" connection
8, usually we use the "rounding" method to omit the tail number for a number of approximations.
The method is: look at the last digit of the number, if it is 4 or smaller than 4, round off the tail, and add a counting unit at the end of the number of "10,000" or "100 million"; if it is 5 or larger than 5, add 1 to the first, and then round off the tail, add a counting unit of "10,000" or "100 million"; if it is 5 or larger than 5, add 1 in the first, then round off the tail. Add the unit of measure "ten thousand" or "billion". The result is an approximation, the center should be connected with "≈".
9. The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ... are all natural numbers. One object is not represented by 0. 0 is also a natural number. The smallest natural number is 0. There are no natural numbers, and the number of natural numbers is infinite.
10, China invented in the fourteenth century is still in use today's calculation tool is the abacus. A bead above the abacus represents 5, and a bead below it represents 1.
11. On a calculator, the ON/C key is the on/off and screen clearing key, the CE key is the clearing key, and the AC key is the return to 0 key. ＋The +, -, ×, and ÷ keys are the arithmetic symbol keys.
Unit 2 Measurement of Angles
1. A straight line has no endpoints and can extend indefinitely to both ends; its length cannot be measured.
2. A ray has an endpoint and can extend indefinitely to one end; its length cannot be measured.
3. A line segment has two endpoints and its length can be measured.
4. Extending one end of a line segment infinitely gives a ray. Extend both ends of the line segment infinitely and you get a straight line. Both the line segment and the ray are parts of a straight line.
5. You can draw an infinite number of lines and rays past one point. Only one line can be drawn past two points.
6. The figure formed by two rays from a point is called an angle. This point is the (vertex) of the angle, the two rays are the ( side ) of the angle. Angles are usually represented by the symbol ("∠").
7, the size of the angle has nothing to do with the length of the two sides of the angle drawn, the size of the angle depends on the size of the two sides of the angle forked, the larger the two sides of the angle forked, the larger the angle.
8, the unit of measurement of the angle is "degrees", expressed in the symbol "°".
9, the protractor is divided equally into 180 equal parts of a semicircle, the size of the angle of each part is 1 degree, recorded as "1 °".
10. The opposite angles are equal.
11. The sum of the three angles of a triangle is 180 degrees. The sum of the four angles of a quadrilateral is 360 degrees.
12, A right angle is equal to 90 degrees, a flat angle is equal to 180 degrees, and a perimeter angle is equal to 360 degrees.
13, 1 flat angle = 2 right angles. 1 circumflex angle = 2 flat angles = 4 right angles.
14, acute angles are less than 90 degrees. An obtuse angle is greater than 90 degrees and less than 180 degrees;
15, acute angle < right angle < obtuse angle < flat angle < circumflex angle 1 hour,
16, the hour hand turns a large square, the angle to which it is opposite is 30 °; the minute hand turns around, the angle to which it is opposite is 360 °
Unit 3 Three-digit times two-digit numbers
1. In three-digit times two-digit numbers, first multiply the three-digit number by the number in the first digit of the two-digit number, then multiply the three-digit number by the number in the tenth digit of the two-digit number. Finally, add up their products.
2, the end of the factors have 0 multiplication: write the vertical formula to the number in front of 0 alignment, only multiply the number in front of 0; two factors at the end of a **** a number of 0, in the multiplication of the end of the product of a number of 0.
3, the rule of change of the product:
① a factor remains unchanged, the other factor to expand (or reduce) a number of times, the product to expand (or reduce) the same number of times. .
Example 1: It is known that: A × B = 215, then A × B × 2 = ( ).
This is expanding B by a factor of 2 and the product should also be expanded by a factor of 2. That is, 215 × 2 = 430, so A × B × 2 = (430).
Example 2: It is known that 2 x A x B = 200, so A x B = ( ).
This is shrinking A by a factor of 2, and the product should also be shrunk by a factor of 2. That is, 200 ÷ 2 = 100, so A × B = (100 ).
② One factor is enlarged or reduced by a number of times and the other factor is reduced or enlarged by the same number of times and the product remains the same.
For example: It is known that A × B = 510, if A is enlarged by 5 times and B is reduced by 5 times, the product is ( 510 ).
③ If one factor is expanded by m times and the other factor is expanded by n times, the product is expanded by m × n times.
④ If one factor is reduced by m times and the other factor is reduced by n times, the product is reduced by m × n times.
④ If one factor is expanded by a factor of m and the other factor is reduced by a factor of n, the product is expanded by a factor of m ÷ n if m > n. If m < n, the product is reduced by a factor of m × n. If m > n, the product is expanded (m ÷ n) times. If m < n, the product is reduced (n ÷ m) times.
6. Speed × time = distance traveled Route ÷ time = speed Route ÷ speed = time
Unit 4 Parallelograms and Trapezoids
1. Two lines that do not intersect each other in the same plane are called parallel lines, and they can also be said to be parallel to each other.
2, in the same plane if two lines intersect at right angles, that is, the two lines are perpendicular to each other, one of the lines is called the plumb line of the other line, the intersection of the two lines is called the foot of the plumb line.
3. If two lines are parallel to a third line, then the two lines are also parallel to each other.
4. If both lines are perpendicular to the third line, then these two lines are also (parallel to each other).
5. The shortest (perpendicular) line drawn from a point outside the line to this line is called the (distance) from this point to the line. The distance between parallel lines (everywhere equal).
6. Rectangle: opposite sides are equal, all four angles are right angles, and each of the two sets of opposite sides are parallel.
7. Perimeter of a rectangle = (length + width) × 2; Area of a rectangle = length × width;
8. Square: all four sides are equal, all four angles are right angles, and each of the two sets of opposite sides are parallel.
9. Perimeter of a square = side length × 4; area of a square = side length × side length.
10 A quadrilateral in which each of the two sets of opposite sides are parallel is called a parallelogram. It is characterized by equal opposite sides and equal opposite angles. Each of the two sets of opposite sides is parallel.
11 A quadrilateral with only one set of opposite sides parallel is called a trapezium. It is characterized by: only one set of opposite sides are parallel and the other set of opposite sides are not parallel. The parallel sides are called the base of the trapezoid, where the long side is called the bottom; the non-parallel sides are called the waist; the distance between the two bases is called the height of the trapezoid.
12. A square is a special rectangle; rectangles and squares are special parallelograms.
13, parallelograms are easily deformed and have the property of instability.
14, from a point on one side of a parallelogram to the opposite side of a vertical line, the line between this point and the foot of the vertical line is called the height of the parallelogram, the foot of the side is called the base of the parallelogram.
15. A trapezoid with two equal waists is called an isosceles trapezoid. The two base angles of an isosceles trapezoid are equal.
16. Two identical trapezoids can be put together to form a parallelogram.
17. Two identical triangles can be put together to form a parallelogram.
18, Among the figures we have studied, rectangles, squares, isosceles trapezoids and rhombuses are symmetrical figures.
19, over a point outside a line can only draw a plumb line of a known line;
20, over a point outside a line can only draw a parallel line of a known line.
21,
Unit 5 division is two-digit division
1, division rules: division is two-digit division, the first two divisors try to divide the first two divisors, if the first two are not enough to divide, try to divide the first three divisors, divided into which, the quotient will be on the top of which, each time you divide the remainder must be smaller than the divisor.
2, the divisor is a two-digit divisor, generally regarded as the divisor and it is close to the whole ten to try to quotient; try to quotient large to adjust the small, try to quotient small to adjust the large. Until the remainder is smaller than the divisor.
3, three-digit divided by two-digit, the quotient may be one-digit, may be two-digit
4, business invariant nature:
① in the division method, the divisor and divisor multiplied (or divided) by a few (except for 0), the quotient is unchanged.
② in the division, the divisor remains unchanged, the divisor multiplied (or divided) by a few (except 0), the quotient should also be multiplied (or divided) by a few.
③ In division, the divisor remains the same and the quotient is divided (or multiplied) by the number of divisors.
7, the remainder of the division equation: divisor ÷ divisor = quotient ...... remainder
Divided by = quotient × divisor + remainder
Unit 6 Statistics
1, the significance of bar charts: bar charts are a unit of length to indicate the number of a certain number of units, depending on the number of Draw straight bars of different lengths, and then put these bars in a certain order. The advantage of the bar chart is that it is easy to see how many of the various quantities.
2, the characteristics of bar charts:?
(1) can make people see the size of each data at a glance.?
(2) easy to compare the differences between the data.
3. The statistical charts we have learned are horizontal bar charts, vertical bar charts, and univariate and compound statistical charts.
4, retest statistical charts are generally composed of chart numbers, graphs, chart items, chart notes and so on. In the administrative vocational aptitude test in the common bar charts, fan-shaped statistical charts, folded statistical charts and mesh statistical charts.