1, stationery store (decimal times integer)

2. Decimal point movement (the law of decimal point size change caused by decimal point position movement)

3. Street Park (the relationship between the decimal places of two multipliers and the decimal places of the product)

4. Packaging (vertical calculation of decimal multiplication)

5. The slowest crawling mammal (vertically calculating decimal multiplication and decimal estimation)

6. Hand in hand (mixed operation and simple calculation of decimal multiplication)

Key points of knowledge

Importance of decimal multiplication

1, decimal times integer and integer multiplication have the same meaning. It can be said that it is a simple operation to find the sum of several identical addends, and it can also be said that it is an integer multiple of this decimal. For example, 2.3×5 means what is the sum of five 2.3. You can also express how many times 2.3 is.

The meaning of multiplying decimal by decimal is to find a few tenths and a few percent of a number.

2. Variation law of multiplication: ① In multiplication, one factor is expanded to the original m(m≠0) times, another factor is expanded to the original n(n≠0) times, and the product is expanded to the original m×n times. ② In multiplication, one factor is reduced to (m≠0) times, the other factor is reduced to (n≠0) times, and the product is expanded to multiple times. (3) In multiplication, one factor is expanded to the original n times (or reduced to the original n times) (n≠0), and the other factor is reduced to the original n times (or expanded to the original n times), and the product remains unchanged.

3. When one factor is less than "1", the product is less than another factor. When one factor is greater than "1", the product is greater than another factor. When one factor is equal to "1", the product is equal to another factor.

The law of decimal size change caused by decimal position movement

1, the change law of decimal size caused by decimal position movement: the decimal point moves one, two and three places to the left ... this number is reduced to the original, ... the decimal point moves one, two and three places to the right ... this number is extended to the original 10 times, 100 times, 1000 times.

2. Move the decimal point to the right. When the number of digits is not enough, add a "0" to make up the position. After the decimal point is moved, the "0" in front of the highest digit of the integer should be removed; The decimal point is moved to the left, and "0" is added when the number of digits is not enough, and the decimal point is added. If there is no number in the integer part, it is represented by "0". If there is a 0 after the decimal point, the "0" at the end should be removed according to the nature of the decimal point.

3. Relationship between decimal places of product and multiplier: In decimal multiplication, two multipliers * * * have several decimal places, and the product has several decimal places.

Decimal multiplication law

1. To calculate the decimal multiplication, first calculate the product according to the law of integer multiplication, and then look at a factor * * *, how many decimal places there are, and count from the last digit of the product to the left and point to the decimal point. The result can be simplified.

2. Decimal multiplication estimation: first round two factors to keep integers, and then multiply them.

3. The operation order of decimal elementary arithmetic is the same as that of integer elementary arithmetic: operation at the same level, from left to right; Two-stage operation, first two and then one; Parentheses, first inside and then outside.

The law of integer operation still applies to decimal operation. Such as the associative law, commutative law and distributive law of multiplication. Wait a minute.

Decimal multiplication

1, decimal times integer: a simple operation to find the sum of several identical addends.

For example, 1.53 indicates how many times 1.5 is or the sum of three 1.5.

Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; Look at a factor * * *, how many decimal places there are, and count the decimal points from the right side of the product.

2. Decimal multiplied by decimal: it means finding the fraction of this number.

For example: 1.50.8 is 1.5. What is eight tenths?

1.5 1.8 is 1.8 times 1.5. What is it?

Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; Look at a factor * * *, how many decimal places there are, and count the decimal points from the right side of the product.

Note: In the calculation results, the 0 at the end of the decimal part should be removed to simplify the decimal; When the number of decimal places is not enough, use 0 to occupy the place.

3. Rule (1): a number (except 0) is multiplied by a number greater than 1, and the product is greater than the original number;

A number (except 0) is multiplied by a number less than 1, and the product is less than the original number.

4. There are usually three ways to find the approximate value:

(1) rounding method; (2) into law; (3) Tailing method

5. Calculate the amount of money, and keep two decimal places, indicating that the calculation has reached the point. Keep one decimal place, indicating that the angle has been calculated.

6. The order of four decimal operations is the same as that of integers.

7, operation law and nature:

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

Subtraction: Subtraction property: A-B-C = A-(B+C) A-(B-C) = A-B+C.

Multiplication: Multiplication commutative law: ab=ba Multiplication associative law: (ab)c=a(bc) Multiplication distributive law: (a+b)c=ac+bc(a-b)c=ac-bc.

Division: nature of division: abc=a(bc)

Decimal division

8. Significance of fractional division: Know the product of two factors and one of them, and find the operation of the other factor.

For example, 0.60.3 represents an operation to find another factor by knowing the product of two factors 0.6 and one factor 0.3.

9. Calculation method of decimal divided by integer: decimal divided by integer, and then divided by integer. The decimal point of quotient should be aligned with the decimal point of dividend. The integer part is not divided enough, quotient 0, decimal point. If there is a remainder, add 0 and divide it.

10. Division calculation method with divisor as decimal: first expand the divisor and dividend by the same multiple to make the divisor an integer, and then calculate according to the fractional division law with divisor as an integer.

Note: If there are not enough digits in the dividend, make up the dividend with 0 at the end.

1 1. In practical application, the quotient obtained by fractional division can also be rounded to a certain number of decimal places as needed to obtain the approximate value of the quotient.

12, the change law of division: ① quotient invariance: the dividend and divisor are simultaneously expanded or reduced by the same multiple (except 0), and the quotient remains unchanged.

(2) The divisor remains the same, the dividend expands, and the quotient expands. ③ The dividend is constant, the divisor decreases and the quotient expands.

13, cyclic decimal: the decimal part of a number. Starting from a certain number, one number or several numbers appear repeatedly in turn. Such decimals are called cyclic decimals. Circular part: the decimal part of a circular decimal, which is a number that appears repeatedly in turn. For example, the period of 6.3232 is 32.

14, the number of digits in the decimal part is a finite decimal, which is called a finite decimal. The number of digits in the decimal part is infinite decimal, which is called infinite decimal.