Positive integers, 0, negative integers, positive fractions and negative fractions can all be written in the form of fractions, and such numbers are called rational numbers. The decimal part of a rational number is a finite decimal or a cyclic decimal. Real numbers that are not rational numbers are called irrational numbers.
Irrational number, also known as infinite acyclic decimal, cannot be written as the ratio of two integers.
If written in decimal form, there are infinitely many digits after the decimal point, which will not cycle. Common irrational numbers include the square root, π and E of incomplete square numbers. Another feature of irrational numbers is the expression of infinite connected fractions. Irrational numbers were first discovered by a disciple of Pythagoras.
The difference between irrational numbers and rational numbers:
1, the two concepts are different.
Rational number is a general term for integers and fractions, positive integers and fractions are called positive rational numbers, and negative integers and fractions are called negative rational numbers. So the number set of rational numbers can be divided into positive rational numbers, negative rational numbers and zero.
Irrational number, also known as infinite acyclic decimal. Simply put, an irrational number is an infinite cyclic decimal with 10 as the base, such as pi and root number 2.
They are different in nature.
The essence of rational number is the ratio of integer a to integer b, for example, 3 to 8, usually A to B.
The essence of irrational number is a number composed of the ratio or fraction of integers.
3. The scope of the two is different.
The set of rational numbers is an extension of the set of integers. In the rational number set, four operations can be performed: addition, subtraction, multiplication and division.
Irrational number refers to a number that cannot be expressed as the ratio of two integers within the real number range.