1, the minimum number of digits is 1, and the minimum natural number is 0.
2. Meaning of decimals: Divide the integer "1" into 10, 100, 1000 ... These scores or fractions can be expressed in decimals.
3. The decimal point has an integer part on the left, a decimal part on the right, followed by decimals, percentiles and thousandths.
Integers and decimals are numbers written in decimal notation.
5. Properties of decimals: Add 0 or remove 0 at the end of decimals, and the size of decimals remains unchanged.
6. Move the decimal point to the right by one, two and three places ... The original number is enlarged by 10 times, 100 times and 1000 times respectively.
The decimal point is shifted to the left by one place, two places and three places ... The original number is reduced by 10 times, 100 times and 1000 times respectively.
Second, the divisibility of numbers.
1, multiple, factor: A÷B=C, a, b, c are all integers, so we say that a can be divisible by b or b can be divisible by a ... If a can be divisible by b, then A is called a multiple of B and B, which is called a factor of a. ..
2. The number of multiples of a number is infinite, the minimum multiple is itself, and there is no maximum multiple. The number of factors of a number is limited, the smallest factor is 1, and the largest factor is itself. A number is both a factor of itself and a multiple of itself.
3. According to whether it can be divisible by 2, natural numbers that are not 0 are divided into even numbers and odd numbers. Numbers that are divisible by 2 are called even numbers, and numbers that are not divisible by 2 are called odd numbers.
4. According to the number of a number factor, non-zero natural numbers can be divided into three categories: 1, prime number and composite number.
Prime number: A number is called a prime number if it has only two factors: 1 and itself. Prime numbers have two factors. Composite number: A number is called a composite number if it has other factors besides 1 and itself. A composite number has at least three factors. The smallest prime number is 2 and the smallest composite number is 4.
5. The prime numbers in1~ 20 are: 2,3,5,7, 1 1, 13, 17, 19.
1~20 is "4, 6, 8, 9, 10, 12, 14, 15, 16, 18.
1' is neither a prime number nor a composite number.
Characteristics of numbers that are multiples of 6,2: The numbers in a unit are 0,2,4,6 and 8.
The characteristic of a number that is a multiple of 5: the number in each bit is 0 or 5.
Characteristics of numbers that are multiples of 3: the sum of the numbers on each digit is multiples of 3.
Characteristics of numbers that are multiples of 3 and 5: the number in a unit is "5".
7. Common factor, common multiple: The common factor of several numbers is called the common factor of these numbers; The largest one is called the greatest common factor of these numbers. The common multiple of several numbers is called the common multiple of these numbers; The smallest one is called the least common multiple of these numbers.
8. Find the greatest common factor and the least common multiple of two numbers in the general relationship by short division; The greatest common divisor of two numbers of coprime relation is 1, and the least common multiple is the product of two numbers; In the multiple relation, the greatest common factor of two numbers is decimal, and the smallest common multiple is large.
Three or four operations
1, one addend = and-the other addend is minuend = difference+meiosis = minuend-difference.
One factor = product/dividend of another factor = quotient × divisor = dividend/quotient.
2. Among the four operations, addition and subtraction are called primary operations, and multiplication and division are called secondary operations.
3, the operation law:
(1) additive commutative law: a+b=b+a multiplicative commutative law: a× b = b× a.
When two numbers are added, the positions of addends are exchanged, and their sum remains the same.
When two numbers are added, the position of the exchange factor remains unchanged.
(2) Additive associative law: (a+b)+c=a+(b+c) Multiplicative associative law: (a×b)×c=a×(b×c).
Add three numbers, first add the first two numbers and then the third number; Or add the last two numbers first, and then add them to the first number, and their sum remains the same.
Multiplication of three numbers: first multiply the first two numbers and then multiply the third number; Or multiply the last two numbers first, and then multiply them with the first number, and their products remain unchanged.
(3) Multiplicative distribution law: (a+b) × c = a× c+b× c.
Multiply the same number by the sum of two numbers, you can multiply the two addends by this number respectively, and then add the two products, and the result remains the same.
(4) nature of subtraction: a-b-c=a-(b+c) nature of division: a÷b÷c=a÷(b×c).
Subtracting two numbers in a row from a number is equivalent to subtracting the sum of two subtractions from this number.
A number divided by two consecutive numbers is equal to the product of this number divided by two divisors.