1. 1 positive and negative numbers are called negative numbers after adding the negative sign "-"to the numbers other than 0. It has the opposite meaning to negative number, that is, I learned that numbers other than 0 are called positive numbers (sometimes "+"is added before positive numbers as needed). 1.2 Rational numbers Positive integers, 0 and negative integers are collectively called integers, and positive and negative fractions are collectively called fractions. Integers and fractions are collectively called rational numbers. Numbers are usually represented by points on a straight line, which is called the number axis. Three elements of number axis: origin, positive direction and unit length. Take any point on a straight line to represent the number 0, and this point is called the origin. Numbers with only two different signs are called opposites. (Example: the reciprocal of 2 is-2; The antonym of 0 is 0) The distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A, and it is recorded as |a|. 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. Two negative numbers, the larger one has the smaller absolute value. Addition and subtraction of rational numbers 1.3 rational number addition rule: 1. Add two numbers with the same sign, take the same sign, and then add the absolute values. 2. Add two different symbols with different absolute values, take the symbol of the addend with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value. Two opposite numbers add up to 0. When a number is added with 0, it still gets this number. Rule of rational number subtraction: subtracting a number is equal to adding the reciprocal of this number. Multiplication and division of rational numbers 1.4 rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0. Two numbers whose product is 1 are reciprocal. Rational number division rule: dividing by a number that is not equal to 0 is equal to multiplying the reciprocal of this number. Divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Divide 0 by any number that is not equal to 0 to get 0. The operation of finding the product of n identical factors is called power, and the result of power is called power. In the n power of a, a is the base and n is the exponent. The odd power of a negative number is negative and the even power of a negative number is positive. Any power of a positive number is a positive number, and any power of 0 is 0. Scientific counting method is used to express numbers greater than 10 as the n power of a× 10. From the first non-zero digit to the last digit on the left of a number, all digits are valid digits of this number.