1, 0 is neither positive nor negative. Positive numbers are all greater than 0, and negative numbers are all less than 0. Usually, positive numbers and negative numbers represent two quantities with opposite relations. If the profit is represented by a positive number, then the loss is represented by a negative number; If it is above sea level, it is represented by a positive number; If it is below sea level, it is represented by a negative number. The boiling point of water is 100℃ and the freezing point of water is 0℃.

2. When calculating the area of irregular figures, those with less than one grid are regarded as semi-grids. Count full squares first, then half squares.

3. The perimeter of the rectangle = (length+width) ×2 The area of the rectangle = length × width.

Perimeter of a square = side length × area of four squares = side length × side length

4. Cut along any height of the parallelogram, and then move it to form a rectangle. The length of the rectangle is equal to the base of the parallelogram, and the width of the rectangle is equal to the height of the parallelogram. Because the area of a rectangle = length× width, the area of a parallelogram = bottom× height, and S=a×h is represented by letters.

5. Assemble two identical triangles into a parallelogram, the base of which is equal to the base of the triangle, and the height of the parallelogram is higher than that of the triangle. The area of the assembled parallelogram is twice that of each triangle, and the area of each triangle is half that of the assembled parallelogram. Because the area of parallelogram is equal to base × height, the area of triangle is equal to base × height ÷2. Use letters to represent S=a×h÷2. Two triangles with equal base and equal height have the same area.

6. Draw the largest triangle in the parallelogram, and the area of this triangle is equal to half the area of this parallelogram.

Nail a rectangular frame with thin wooden strips. If you pull it into a parallelogram, its perimeter remains the same and its area becomes smaller, because the bottom remains the same and its height becomes smaller.

If parallelograms are drawn into rectangles, their perimeters remain unchanged and their areas become larger.

7. Assemble two identical trapezoids into a parallelogram. The base of the parallelogram is equal to the sum of the upper and lower bases of the trapezoid, and the height of the parallelogram is higher than that of the trapezoid. The area of assembled parallelogram is twice that of each trapezoid, and the area of each trapezoid is half that of assembled parallelogram. Because the area of parallelogram = bottom × height, and the area of trapezoid = (upper bottom+lower bottom) × height ÷2 letters mean S = (a+b) × h ÷ 2.

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

Fractions with denominator of 10 are written as decimals, indicating tenths.

Fractions with denominator of 100 are written in two decimal places, indicating a few percent.

Fractions with denominator of 1000 are written in three decimal places, indicating how many thousandths.

The first digit to the left of the decimal point is a number, and the counting unit is (1).

The second digit to the left of the decimal point is ten, and the counting unit is ten (10).

The first digit to the right of the decimal point is one tenth, and the counting unit is one tenth (0. 1).

The second digit to the right of the decimal point is the percentile, and the counting unit is one hundredth (0.0 1).

The third digit to the right of the decimal point is one thousandth, and the counting unit is one thousandth (0.005438+0).

The highest digit of the decimal part is ten digits, and the largest counting unit is one tenth. The propulsion rate between two adjacent counting units is 10.

9. 1 includes (10) 0. 1 (one tenth) and 0. 1 (one tenth) and10.01(one percent).

10, the nature of decimal: add "0" or remove "0" at the end of decimal, and the size of decimal remains unchanged.

1 1, with "ten thousand" as the unit: 1, and put a decimal point after ten thousand digits; 2. Add the word "ten thousand". Use the "=" symbol. Take "hundred million" as the unit: 1, and add a decimal point after the hundred million digits; 2. Add a word "billion". Use the "=" symbol. Note: Rewriting cannot change the size of the original number.

Omit the mantissa after ten thousand: depending on the number of "thousands", use rounding method to get an approximate value. Use "". Mantissa after omitting 1 100 million: According to the digits of "1100 million", an approximate value is obtained by rounding. Use "".

Keep an integer, that is, accurate to one place, depending on the first place (tenth place) of the decimal part.

Keep a decimal place, that is, accurate to ten places, depending on the second place (percentile) of the decimal part.

Keep two decimal places, that is, accurate to one percent, depending on the third decimal place (one thousandth).

Note: When representing approximate values, the "0" at the end shall not be deleted.

For example, decimals with two decimal places are 1 and 50, and the "0" at the end cannot be removed. 1, 50 and 1.5 are equal in size, but different in accuracy. 1.50 means accurate to one hundredth, while 1.5 means accurate to one tenth, so the "0" at the end of 1.50 must not be removed when representing the divisor.

12. When calculating decimal addition and subtraction, the decimal points should be aligned, that is, the same digits should be aligned.

13, find the law: 1, find the cycle; 2. Cycle number; 3. What is the remainder? 4. To calculate the number of items in each project, it can be done in three steps: (1) each item is a group; (2) There are several in each group; Multiply the number of groups (3) by 1 * * *, and finally add the remainder, which is equal to how many there are in a * * *.

14. Problem-solving strategy: List all possible situations one by one. The skill of listing is to consider the larger numbers first (put them in the first row).

15. When calculating fractional multiplication (1), calculation: according to the law of integer multiplication; (2) Look: How many decimal places does one of the two factors have? (3) Number: Count several numbers from the end of the product; (4) Point: Point decimal point; (5) Go: Remove 0 after the decimal point.

16, a decimal is multiplied by 10, 100, 1000 ... just move the decimal point to the right by one, two or three places. ...

Divide a decimal by 10, 100, 1000 ... just move the decimal point one, two or three places to the left. ...

17, 1 square kilometer is the area of a square with a side length of 1000 meters, which is equal to 1000000 square meters. 1 hectare is the area of a square with a side length of 100 m, which is equal to 10000 m2. 1 km2 = 100 hectare. 1 ha = 100 ha = 10000 m2.

18, the arithmetic of integer addition, subtraction, multiplication and division is also applicable to decimals.

Additive commutative law: a+b=b+a Addition Law: (a+b)+c= a +(b+c)

Multiplicative commutative law: a×b=b×a additive associative law: (a×b)×c= a ×(b×c)

The essence of subtraction: a-b-c = a-(b+c)

The nature of division: a÷b÷c = a÷(b×c)

19, divisor is fractional division. First, look at how many decimal places the divisor * * * has, and then expand the divisor and divisor at the same time according to the law of constant quotient, making it a division of divisor into integer. The key point is to align the decimal point of the quotient with the decimal point of the current divisor and add "0" endlessly to continue the division (only one 0 can be added at a time). Which number is not quotient enough?

20. When one factor is not 0 and the other factor is greater than (less than) 1, the product is greater than (less than) the first factor. (If a factor is multiplied by a number greater than 1, the product will become larger and larger; Multiply by a number less than 1 and the product will get smaller and smaller. )

A×(> 1)(>)A A×(< 1)(