Knowledge points of Understanding Large Numbers, the first volume of fourth grade mathematics
1.1010,000 is 100,000,1010,000 is 1 million,101 million is 10 million,1010 million is 100 million.
The advance rate between every two adjacent counting units is "10". This counting method is called decimal counting method.
Special attention: the difference between counting units and numbers.
2. When using numbers to represent numbers, these counting units should be arranged in a certain order, and their positions are called numbers.
3. Number of digits: A number contains several digits, that is, several digits. For example, 652 100 is a six-digit number.
According to our country's counting habit, every four digits are counted from the right.
5. How to pronounce hundreds of millions or more:
(1) Grading first, starting from high reading. Read level 100 million, then level 10,000, and finally level 1.
(2) Billions should be read according to the pronunciation of billions, and then the word "billion" should be added at the end. Ten thousand series should be read according to the reading method of ten thousand series, and then the word "ten thousand" should be added after it.
No matter how many zeros there are at the end of each level, don't read them. Other numbers have a "0" or several "0" in succession, all of which are read only.
6, hundreds of millions of words:
(1) Write from bits, first write 100 million levels, then write 10,000 levels, and finally write one level.
(2) If there is no unit, just write 0 on the number.
7, compare the size of the quantity:
The two numbers are different, the one with more numbers is bigger and the one with fewer numbers is smaller.
(2) Two numbers with the same number of digits, starting from the number of digits, the number with the largest number of digits is larger. If the numbers on the numbers are the same, compare the numbers on the next number until the size is compared.
8. Number of rewrites:
Rewrite it into a number in the unit of "10000" or "10000000". Draw a grading line first, divide the integer 10 thousand or integer 100 thousand into four levels, then omit four zeros from each level and replace them with the word "100 thousand"
9. Find out the approximate figures:
The mantissa after omitting ten thousand digits depends on the number on one thousand digits; The mantissa after omitting 1 100 million bits depends on the number on1100 million bits.
When calculating the divisor by "rounding", it depends on whether the number of the omitted mantissa part is less than 5 or equal to or greater than 5. If it is less than 5, the mantissa is discarded and rewritten as a corresponding number of zeros; If it is equal to or greater than 5, advance 1, then discard the mantissa and rewrite it as a corresponding number of zeros.
10, indicating the number of objects: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... are all natural numbers. There is no object, which is represented by 0, and 0 is also a natural number. All natural numbers are integers.
1 1, the smallest natural number is 0, there is no natural number, and the number of natural numbers is infinite.
12, calculator ON/CE: switch the clear screen key to clear the contents on the display screen.
AC: Clear the key, clear everything.
DEL: Clear the wrong number or operation symbol just entered.
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.
Mathematics learning methods and skills
One: Take notes
This method is actually very common and simple, but it is difficult for many students to do it. Taking notes has many advantages. First, you can record the essence of the teacher for review. Second, it can train students' writing ability. Thirdly, it can help students develop their learning ability in listening and writing, which is very effective in improving learning efficiency.
Two: wrong title book
Many children are sloppy, but some sloppy are actually caused by students' unclear understanding of knowledge points. Such a topic must be recorded. There are also traps deliberately designed by questioners, which can also be recorded and reviewed regularly. After a long time, many carelessness will naturally be avoided.
Three: study group
Sharing good test questions, methods, skills and experiences with group members on a regular basis can not only increase the affection between classmates, but also learn new things in the process of making friends, improve learning efficiency, cultivate cooperation spirit and enhance coordination ability.
Four: Subject Classification Book
I like the wrong problem book and record the problems I have done. Classification refers to dividing the problems I have done into several categories, one of which is extremely simple and can be read by myself. One kind is difficult, which requires thinking to find a breakthrough, and the other kind is difficult, which requires a lot of comprehensive knowledge and reasoning to solve. The latter two should be the focus of our records. In the process of classifying the test questions, students naturally enhance their further understanding of the test questions.
Five: New solutions to old problems
Look through the original questions from time to time, but the key point is to think about whether there are new ideas and skills for solving problems. This increasing thinking is conducive to the formation of students' thinking habits, as well as the formation of students' divergent thinking, examining ideas from multiple angles and using new knowledge to solve problems at any time.
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