1. Decimal multiplication by integer (Decimal multiplication is calculated by using the law of product change caused by factor change)
Knowledge point one:
1. To calculate decimal addition, first align the decimal points, and then add the numbers with the same digit.
2. Calculate the end alignment of decimal multiplication, and calculate according to the rules of integer multiplication.
Knowledge point 2:
Multiplication with 0 after the decimal point in the product. After calculating the product of decimal times integer, 0 appears at the end of decimal of the product, and then the 0 at the end of decimal should be removed according to the nature of decimal. For example, 3.60 "0" should be crossed out.
Knowledge point 3:
If the number of decimal places of the multiplied product is not enough, you should add 0 in front and then add the decimal point. For example, 0.02x2 = 0.04.
Knowledge point 4:
When calculating decimal multiplication with zero at the end of integer factor, align the rightmost digit of integer digits that is not zero with the end of decimal.
Thinking:
What's the difference between decimal times integer and integer times integer?
There is a factor in 1, and a decimal multiplied by an integer is a decimal, so the product is generally a decimal.
If there is a 0 at the end of the sum part of the product in decimal multiplication, the 0 at the end of the decimal can be removed according to the basic properties of the decimal, but it cannot be removed in integer multiplication.
Second, decimal times decimal.
Knowledge point one:
Relationship between factor and product decimal places: factor * * has several decimal places, and product also has several decimal places.
Knowledge point 2:
General calculation method of decimal multiplication:
First calculate the product by integer multiplication, and then put the decimal point on the product point (see a factor * * *, how many decimals there are, output several numbers from the right side of the product and put the decimal point on it). ) The product has insufficient decimal places. Add 0 in front of the product and calculate the decimal point.
Knowledge point 3:
Checking calculation method of decimal multiplication
1. Multiplies the position of the factor.
2. Check with a calculator.
Third, the approximate quantity of products.
Knowledge point one:
Calculate the product first, then look at the next number to keep, and then find the result by rounding, which is represented by an equal sign.
Knowledge point 2:
If the divisor is 9 and the next digit is greater than 5, you need to enter 1, that is to say, you need to enter 1 in turn, and use 0 to occupy the position. If 6.597, keep two digits as 6.60.
Fourth, multiply, multiply and subtract.
Knowledge point one:
Decimal multiplication should be calculated from left to right.
Knowledge point 2:
The order of decimal multiplication and addition is the same as that of integer multiplication and addition. Multiply first and then add.
The commutative law, associative law and distributive law of integer multiplication are also applicable to fractional multiplication.
Verb (abbreviation of verb) simple operation
The commutative law, associative law and distributive law of integer multiplication are also applicable to fractional multiplication.
When calculating serial multiplication, we can apply multiplication exchange law and association law, first multiply two numbers of several integers, and then multiply another number. When calculating one-step multiplication, we can divide the numbers close to integer ten and integer hundred into the addition and subtraction formulas of integer ten and one digit, and then apply the multiplication distribution law to simplify the calculation.
Some formulas that do not conform to the operation law can also be applied through deformation.
Multiplication and division can also be extended to the corresponding subtraction.
Unit 2 knowledge points of fractional division
1, the meaning of fractional division: know the product of two factors and one of them, and find the operation of the other factor. For example, 2.6÷ 1.3 means that the product of two known factors is 2.6, one of which is 1.3, and the other factor is found.
Calculation method of fractional division:
The calculated divisor is the fractional division of an integer, which is removed by the calculation method of integer division. The decimal point of quotient should be aligned with the decimal point of dividend, and the integer part is not enough. If the quotient is 0, click the decimal point to continue the division; If there is a remainder, add 0 and divide it.
Calculating the divisor is fractional division. First, convert the divisor into an integer, move the decimal point of the divisor to the right by several digits, and move the decimal point of the dividend to the right by several digits. If there are not enough digits, make up the divisor with the 0 at the end, and then calculate by fractional division with the divisor as an integer.
2, the approximate method:
There are three methods to approximate: ① rounding; 2 enter one; 3 ending.
In general, rounding method is used when taking the divisor as required, and one-step method and tail cutting method are used when solving practical problems.
When you take the divisor of the quotient, you must divide it by the next digit, and then round it off to take the divisor. When there is no requirement, except for the inexhaustible ones, two decimal places are generally reserved.
3. 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. Numbers that appear repeatedly in turn are called cyclic knots of such cyclic decimals.
4. Representation of cyclic decimals:
One is represented by ellipsis, which means to write two complete loop segments followed by ellipsis. Such as: 0.3636... 1.5587 ...
Another method is shorthand: just write a set of circular parts, and then dot the first and last numbers of the circular parts. Such as: 12.
5. Finite decimals: The digits in the decimal part are finite decimals, which are called finite decimals.
6. Infinite decimal: The digits in the decimal part are infinite decimal, which is called infinite decimal.
Unit 3 observing the knowledge points of objects
1, observing objects from different angles may lead to different shapes; When observing a cuboid or cube, you can see at most three faces from a fixed position.
2. The front, side and back are relative and change with the change of observation angle. By observing, imagining and guessing, we can cultivate our spatial imagination and thinking ability and correctly identify the shape of simple objects observed from the front, side and above.
3. Construct spatial imagination:
(1), two identical cubes are arranged side by side, and it is required to imagine what they look like from different angles (emphasizing the coincidence of left and right, so only one square can be seen).
(2) Arrange a cube and a cylinder side by side and imagine what it looks like from different angles.
4, hands-on operation, thinking expansion
Use five small cubes to put the figure from the front (you can put it in several different ways). (How many different ways, how many small cubes are needed at least, and how many small cubes can only be used at most. )