1. rational number:
(3) Note: among rational numbers, 1, 0 and-1 are three special numbers with their own characteristics; These three numbers divide the numbers on the number axis into four areas, and the numbers in these four areas also have their own characteristics;
(4) Natural numbers? 0 and positive integer; a & gt0 ? A is a positive number; a & lt0 ? A is a negative number;
a≥0？ Is it a positive number or 0? A is negative; a≤ 0？ Is it negative or 0? A is a non-positive number.
2. Number axis: The number axis is a straight line that defines the origin, positive direction and unit length.
3. The opposite number:
(1) There are only two numbers with different signs, and we say that one of them is opposite to the other; The antonym of 0 is still 0;
(2) Note: The inverse of a-b+c is-A+B-C; The inverse of a-b is b-a; The inverse of a+b is-a -a-b；;
(3) Is the sum of opposites 0? a+b=0？ A and b are opposites.
4. Absolute value:
(1) The absolute value of a positive number is itself, the absolute value of 0 is 0, and the absolute value of a negative number is its inverse; Note: the absolute value means the distance between the point representing a number on the number axis and the origin;
5. Rational number ratio: (1) The greater the absolute value of a positive number, the greater the number; (2) Positive numbers are always greater than 0 and negative numbers are always less than 0; (3) Positive numbers are greater than all negative numbers; (4) The absolute values of two negative numbers are larger than the size, but smaller; (5) Of the two numbers on the number axis, the number on the right is always greater than the number on the left; (6) large number-decimal number >; 0, decimal-large number < 0.
6. Reciprocal: Two numbers whose product is 1 are reciprocal; Note: 0 has no reciprocal; If a≠0, the reciprocal is; The reciprocal itself is a number of 1; If ab= 1? A and b are reciprocal; If ab=- 1? A and b are negative reciprocal.
7. The rational number addition rule:
(1) Add two numbers with the same symbol, take the same symbol, and add the absolute values;
(2) Add two numbers with different symbols, take the symbol with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value;
(3) Adding a number to 0 still gets this number.
8. Arithmetic of rational number addition:
The commutative law of (1) addition: a+b = b+a; (2) The associative law of addition: (a+b)+c=a+(b+c).
9. Rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number; That is, a-b=a+(-b).
10 rational number multiplication rule:
(1) Multiply two numbers, the same sign is positive, the different sign is negative, and the absolute value is multiplied;
(2) Multiply any number by zero to get zero;
(3) When several numbers are multiplied, one factor is zero and the product is zero; Each factor is not zero, and the sign of the product is determined by the number of negative factors.
1 1 rational number multiplication algorithm;
(1) The commutative law of multiplication: ab = ba(2) The associative law of multiplication: (AB) C = A (BC);
(3) Distribution law of multiplication: a(b+c)=ab+ac.
12. rational number division rule: dividing by a number is equal to multiplying the reciprocal of this number; Note: Zero cannot be divisible.
13. Power Law of Rational Numbers:
(1) Any power of a positive number is a positive number;
(2) The odd power of a negative number is a negative number; Even the power of negative numbers is positive; Note: When n is positive odd number: (-a)n=-an or (a -b)n=-(b-a)n, when n is positive even number: (-a)n =an or (a-b) n = (b-a) n. 。
15. Scientific notation: Write numbers greater than 10 in the form of a× 10n, where a is a number with only one integer digit. This notation is called scientific notation.
16. Approximation precision: a divisor rounded to that bit, that is, the divisor is accurate to that bit.
17. Significant digits: All digits from the first non-zero digit on the left to the exact digit are called significant digits of this approximation.
18. Mixed algorithm: multiply first, multiply then divide, and finally add and subtract; Note: How to calculate simply and accurately is the most important principle of mathematical calculation.
19. special value method: it is a method of substituting numbers that meet the requirements of the topic into speculation to verify the establishment of the topic, but it cannot be used for proof.