Irrational number is a number in real number that cannot be accurately expressed as the ratio of two integers, that is, infinite acyclic decimal. Such as pi, the square root of 2, etc. Rational numbers are fractions and integers, which can be converted into finite decimals or infinite cyclic decimals. For example, 7/22, √ 2 =1.414213562 ... People define irrational numbers as infinite acyclic decimals accordingly.

The importance of mathematics:

Mathematics is a scientific language;

Galileo once said, "Naturally, this book is written in mathematical language. ..... this book is unreadable unless you learn its language first. " The scientific language of mathematics is very precise, which is the characteristic of mathematics.

At the same time, this language is universal. Addition, subtraction, multiplication and division, square root, exponential logarithm, differential integral, constant and so on, although these mathematical languages and symbols may be varied at first, they have long been unified into a fixed style, which is universal all over the world and very convenient for us to master and use.

Mathematics is a powerful tool;

Obviously, mathematics plays an important role in people's daily life and production anytime and anywhere. In modern times, mathematics, as an important weapon of modernization, plays a key and even decisive role in many important fields. China's outstanding achievements in the development of two bombs and one satellite have condensed the efforts of many outstanding mathematicians, which is a prominent example.

Mathematics is a foundation of * * *;

Now, not only in natural science and technical science, but also in economic science, management science and even humanities and social sciences, mathematics has become an indispensable and important foundation in order to accurately and quantitatively consider problems and get a well-founded and regular understanding.

Without the support of mathematics, it is difficult to make great progress in related sciences, and many disciplines (especially many natural science disciplines) have even appeared the trend of mathematicization in recent years.

Mathematics is the key technology;

It seems incredible that mathematics, which used to be completed with a pen and a piece of paper, can become a technology. However, the combination of mathematical ideas and methods with highly developed computing technology does form a technology, and it is a key and realizable technology, which is called "mathematical technology".

The core part of this technology is mathematics. If you take it away, there's only a pile of scrap metal. The advanced CT technology we saw in the hospital is a prominent example. Its essence is to restore the three-dimensional shape of objects in the body by using many plane photos taken by X-rays from different angles, which is completely a mathematical problem.

In this way, the connotation of mathematics is materialized into computer software and hardware, which becomes an important part and key of technology and can be directly transformed into productivity. Now, the saying that "high technology is essentially a mathematical technology" has been recognized by more and more people.