I. Positive Numbers and Negative Numbers

1, previously learned numbers other than 0 with a negative sign "-"in front are called negative numbers.

2. The numbers other than 0 that I learned before are called positive numbers.

3. Zero is neither positive nor negative, and zero is the dividing line between positive and negative numbers.

4. In the same problem, positive numbers and negative numbers have opposite meanings.

Second, rational numbers.

1, positive integers, 0 and negative integers are collectively called integers, and positive and negative fractions are collectively called fractions.

2. Integers and fractions are collectively called rational numbers.

3. Put a number together to form a set of numbers, which is called number set for short.

Third, the number axis

1, and the straight line defining the origin, positive direction and unit length is called the number axis.

2. Function of the number axis: All rational numbers can be represented by points on the number axis.

3. Note: The origin, positive direction and unit length of (1) axis are indispensable.

⑵ The unit length of the same shaft cannot be changed.

4. Attribute: Of the two numbers represented on the (1) number axis, the number on the right is always greater than the number on the left.

(2) Positive numbers are all greater than zero, negative numbers are all less than zero, and positive numbers are greater than negative numbers.

Fourth, the inverse number

1, only two numbers with different signs are called reciprocal.

2. The two points representing the opposite number on the number axis are symmetrical about the origin.

The reciprocal of zero is zero.

Absolute value of verb (abbreviation of verb)

1. The distance between the point representing the number A on the general number axis and the origin is called the absolute value of the number A, and it is recorded as |a|.

2. The absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0.

6. Comparison of rational numbers

1, positive number is greater than 0, 0 is greater than negative number, positive number is greater than negative number.

2, two negative numbers, the absolute value is big but small.

Seven, the addition of rational numbers

1, the addition rule of rational numbers

Add two numbers of (1), take the same sign, and then add the absolute values.

(2) Add two numbers with different absolute values, take the sign of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value.

(3) Two opposite numbers add up to get zero.

(4) When a number is added to zero, the number is still obtained.

2. Arithmetic of rational number addition

(1) additive commutative law: Two numbers are added, the addend positions are exchanged, and the sum is unchanged. That is, a+b = b+a.

(2) The law of addition and association: When three numbers are added, the first two numbers are added, or the last two numbers are added first, and the sum is unchanged. That is, (a+b)+c=a+(b+c)

Eight, subtraction of rational numbers

1, rational number subtraction rule

Subtracting a number is equal to adding the reciprocal of this number. That is, a-b=a+(-b)

Nine, multiplication of rational numbers

1, multiplication rule of rational numbers

(1) Multiply two numbers, the same sign is positive, the different sign is negative, and the absolute value is multiplied.

(2) Any number multiplied by 0 will get 0.

(3) Two numbers whose product is 1 are reciprocal.

(4) Multiply several numbers that are not zero, and when the number of negative factors is even, the product is positive; When the number of negative factors is odd, the product is negative.

(5) When several numbers are multiplied, if one factor is zero, the product is zero.

2. Arithmetic of rational number multiplication

(1) Multiplication Commutativity Law: When two numbers are multiplied, the positions of the exchange factor and the product are equal. Namely ab=ba

(2) Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied first, or the last two numbers are multiplied first, and the products are equal. That is, (ab)c=a(bc)

(3) Multiplication and distribution law: a number is multiplied by the sum of two numbers, which means that this number is multiplied by these two numbers respectively, and then the products are added. That is, a(b+c)=ab+ac.

Division of rational numbers

1, rational number division rule

(1) divided by a number that is not equal to 0 is equal to multiplying the reciprocal of this number.

(2) Zero cannot be divided.

(3) Divide two numbers, the one with the same sign is positive, and the one with different signs is negative, and divide by the absolute value.

(4) Divide 0 by any number that is not equal to 0 to get 0.

Xi。 Power of rational number

1, the operation of finding the product of n identical factors is called power, and the result of power is called power. In, a is called the base and n is called the exponent. When an is regarded as the result of the n power of a, it can also be read as the n power of a. ..

2. The odd power of a negative number is negative, and the even power of a negative number is positive.

3. Any power of a positive number is a positive number and any power of a positive integer is 0.

Twelve, rational number mixed operation operation order

1, calculate the power first, then multiply and divide, and finally add and subtract;

2. Unipolar operation, from left to right;

3. If there are brackets, do the operation in brackets first, and then follow the brackets, brackets and braces in turn.

Thirteen, scientific notation

1, numbers greater than 10 are expressed as a× 10n (where a is a number with only one integer bit and n is a positive integer), and scientific notation is used.

2. Use scientific notation to represent n-bit integers, where the exponent of 10 is n- 1.

14. Approximate values and significant figures

1, which is close to the actual number, but still different from the actual number, is called a divisor.

2. Accuracy: If an approximate number is rounded, it means it is accurate.

3. From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number.

4. For the number a× 10n expressed by scientific notation, its effective number is specified as the effective number in A. ..