The rational set is () A the set of positive and negative numbers B the set of positive integers, negative integers and fractions C the set of integers and fractions D the set of integers and D Set of integers and negative numbers The rational set is () A the set of positive and negative numbers B the set of positive integers, negative integers and fractions C the set of integers and fractions D the set of integers and D A collection of integers and negative numbers

The rational set is () A the set of positive and negative numbers B the set of positive integers, negative integers and fractions C the set of integers and fractions D the set of integers and D Set of integers and negative numbers The rational set is () A the set of positive and negative numbers B the set of positive integers, negative integers and fractions C the set of integers and fractions D the set of integers and D A collection of integers and negative numbers

Set of C integers and fractions

How to judge whether a number is irrational or rational?

The difference between irrational number and rational number
1. When both rational and irrational numbers are written as decimals, rational numbers can be written as integers, decimals, or infinite cyclic decimals, such as 4=4.0,4/5=0.8,1/3=0.33333... An irrational number can only be written as an infinite non-recurring decimal, such as √2=1.414213562... According to this point, irrational numbers are defined as infinite non-recurring decimals.2. An irrational number can not be written as the ratio of two integers. For example, the root number 2 of a fraction is not an integer. By using the main difference between rational numbers and irrational numbers, it can be proved that √2 is an irrational number. It can be proved that √2 is not an irrational number, but a rational number. Since √2 is a rational number, it must be written as the ratio of two integers:√2= p/q. Since p and q have no common cause to be reduced, it can be considered that p/q is the simplest fraction. Let √2=p/q be square to 2=(p^2)/(q^2), i.e.2(q^2)=p^2. Since 2q^2 is an even number, p must be an even number. Let p=2m be q^2=2m^2 from 2(q^2)=4(m^2). Similarly, q must be an even number. Let q=2n. Since p and q are even numbers, they must have a common factor of 2, which contradicts the previous assumption that p/q is the simplest fraction. This contradiction is caused by the assumption that √2 is a rational number. Thus √2 is an irrational number.1. Judge whether a√b is an irrational number (a, B is an integer) If a√b is a rational number, it must be written in the form of the ratio of two integers: a√b=c/d (c/d is the simplest fraction) b=c^a/d^a, i.e. c^a=b*(d^a) c^a must be an integer multiple of b, let c^a=b^n*p, similarly b*(d^a) must be an integer multiple of b, let b*(d^a)=b*(b^m*q). Where p and q are not integer multiple of b, the factor number of b on the left is a multiple of a, and if the equation holds, the factor number of b on the right must be a multiple of a, If and only if b is a complete a-th power, a√b is a rational number, otherwise it is an irrational number.