Basic knowledge points of mathematics in the first volume of the fourth grade
1, meaning of natural number integer
1, 2, 3 ... used to represent the number of objects is called natural number. There is no object, which is represented by 0. 0 is also a natural number. They are all integers.
The smallest natural number is 0, there is no natural number. The number of natural numbers is infinite.
2. Counting units: one (one), ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million, one hundred million … are all counting units. Where "one" is the basic unit of counting.
3. Decimal counting method 10 1 Yes 10, 10 is 100 ... The propulsion rate between every two adjacent counting units is 10. This counting method is called decimal counting method.
4. Numbers
Counting units are arranged in a certain order, and their positions are called numbers.
5. How to read integers: from high to low, read step by step. When reading the 110 million level, first read according to the reading method of the 100 level, and then add a word "100 million" or "10 thousand" at the end. The zeros at the end of each stage are not read, and only a few zeros of other digits are read.
6. Writing of integers: from high to low, writing step by step. If there is no unit on any number, write 0 on that number.
7. How to write more than ten thousand:
(1) A number contains 10,000 levels and 100 million levels, so write it step by step.
(2) When writing numbers, write a few words where the numbers are higher, and write zero placeholders where there is no unit.
8. Compare the size of two numbers:
When the number of (1) digits is different, the number with more digits is large and the number with less digits is small;
(2) If the number of digits is the same, the larger the number of digits, the larger the number; If the first place is the same, look at the next place, and so on.
9, the whole ten thousand, hundreds of millions of rewriting:
(1) is rewritten as a number with "ten thousand" as the unit, four zeros after the ten thousand digits are removed, and a word "ten thousand" is added.
(2) Rewrite it into a number with "100 million" as the unit, remove eight zeros after the hundred million digits, and add a word "100 million".
10, divisor and exact number:
Some figures are preceded by the word "about", which is inaccurate. Numbers like this are called "divisors".
"Rounding method": When taking the divisor, which digit should be reserved as required, and the number after this digit is called "mantissa". If the number of digits of the mantissa is less than 5, the mantissa is removed. If the number of digits of the mantissa is greater than or equal to 5, the mantissa is truncated and "1" is added to its previous digit, which is called rounding.
"Omitting the mantissa after 10,000 bits or 100 million bits to find the divisor" means to accurately (reserve) a number to 10,000 bits or 100 million bits by rounding.
(1) Use "10,000" as the approximate figure, and then decide whether it is "four hospitals" or "five schools" depending on thousands of figures.
(2) The approximate figure of "100 million" depends on the figure of 10 million, and then decide whether it is "four" or "five".
(3) Whether using "10,000" or "100,000,000" as the unit, when writing the divisor, we should use the equal sign (substance) to connect them, and write "10,000" or "100,000" at the end.
1 1. Finding similarities between divisor and rewriting number: Finding divisor and rewriting number means expressing a larger number as an integer "10,000" or "100 million" followed by a word "10,000" or "100 million".
Difference: Finding divisor is to change a number into a divisor, and the size of the number has changed; The rewriting of numbers is just to write a large number into a number with "ten thousand" or "hundred million" as the unit, and the size has not changed.
12, digital coding. Numbers can be used not only to represent quantity and order, but also to encode. The numbers in the code represent specific meanings. The coding is orderly.
Knowledge points of fourth grade mathematics
Algorithms and simple operations
First, the law of addition:
1, additive commutative law: Two numbers are added, the addend positions are exchanged, and the sum is unchanged. a+b=b+a
2, the law of addition and association: three numbers are added, you can add the first two numbers first, and then add the third number; Or add the last two numbers first, and then add the first number, and the sum remains the same. (a+b)+c=a+(b+c)
These two laws of addition are often used together.
For example:165+93+35 = 93+(165+35) What is the basis?
3. The essence of continuous subtraction: one number subtracts two numbers continuously, which is equal to the sum of this number MINUS those two numbers. a-b-c=a-(b+c)
Second, the law of multiplication:
1, multiplication method of substitution: When two numbers are multiplied, the exchange factor position remains unchanged. a×b=b×a
2. Multiplication and association law: When three numbers are multiplied, you can multiply the first two numbers and then the third number, or you can multiply the last two numbers and then the first number, and the product remains unchanged. (a×b)×c=a×(b×c)
These two multiplication laws are often used in combination. Such as: 125×78×8.
3. Multiplication and distribution law: the sum of two numbers is multiplied by one number. You can multiply these two numbers by this number first, and then add up the products.
(a+b)×c=a×c+b×c (a-b)×c=a×c-b×c
Fourth grade, the first volume of mathematics "approximate" knowledge points
Knowledge points of divisor
1, the characteristics of exact number and approximate number.
The exact number is generally in the unit of "one", and the approximate number is in the unit of "ten thousand" or "one hundred million", and the mantissa is omitted.
2. Use rounding method to keep approximate values.
Look at the next number to be reserved according to the requirements in the question. If this number exceeds 5, proceed to the previous number. If it is less than 5, give it up. Regardless of the last few digits of the mantissa. If it is accurate to 10 thousand digits, only a few thousand can be seen, and if it is accurate to 100 million digits, only tens of millions can be seen. Finally, be sure to write the name of the company.
Typical exercise
fill (up) a vacancy
1, a number consists of seven thousands, three hundreds and five tens, and this number is ().
2. From the right, the hundredth place is (), and the fifth place is ().
3. 3465 digits are () digits, which are () digits. "6" is in the () position, which means (). "3" is in the position of (), which means ().
4. There is () ten in 100, () hundred in 1000, and () one in10.
The four digits of 5 are (), and the three digits of 5 are (). Their sum and difference are (). It consists of () thousand, () hundred and () one.
6. The reading method of numbers within10000 is to read in numerical order from () bit; () How many students are there? () thousands; What are the hundreds of students who participated in ()? There are one or two zeros in the middle, which are read-only () zeros; No matter how many zeros () are at the end.
Second, write down the approximate figures of the following figures.
The divisor of 698 is: the divisor of 2956 is:
The divisor of 3 120 is:
The divisor of 1004 is:
Articles related to the important knowledge points of the fourth grade mathematics foundation;
★ Basic knowledge points of mathematics in the first volume of the fourth grade
★ Basic knowledge points of mathematics in the fourth grade of primary school
★ Review the basic knowledge points of fourth grade mathematics.
★ Summary of basic knowledge points of mathematics in grade four
★ Important knowledge points in the first volume of mathematics in the fourth grade of primary school
★ Basic knowledge points of fourth grade mathematics
★ Important knowledge points of fourth grade mathematics
★ Basic knowledge points of mathematics in the fourth grade of primary school
★ Important knowledge points of mathematics in the fourth grade of primary school
★ Summary of basic knowledge points of mathematics in grade four