Types of Numbers 02:10 minutes

Video Transcript

Transcript Types of Numbers

The system of different types of numbers is structured quite the same like the countries and cities all over the world. This is Hayato. He lives in Japan. This is a island nation in East Asia. The Japanese islands are in the Pacific.

To be more precise, we can say Hayato lives in Tokyo. To be even more precise, we can say Hayato lives in the district of Shibuya. There he lives on this street. Hayato lives exactly in this house. What has this to do with the real number system you ask? I will show you!

Whole Numbers

The first numbers that you learned were the natural numbers. These are numbers like 6, 11, 21, 50 and so on. It is like the different houses. All the natural numbers plus Zero belong to the whole numbers. Just like every house belongs to a street.


When we look what comes next, we find the integers. The integers are whole numbers as well as negative numbers. It is like all of the streets in the district of Shibuya.

Rational Numbers

One step further, there are the rational numbers. The rational numbers are positive and negative fractions as well as positive and negative decimals that terminate or repeat.

Note that not every rational number is an integer, but every integer is a rational number. It is like: Not everybody who lives in Tokyo also lives in Shibuya, but everybody who lives in the district Shibuya lives in Tokyo. There isn't just one city in Japan! You can see here is Osaka. Tokyo and Osaka are two separate cities. You cannot be in both places at the same time!

Irrational Numbers

A number can be a rational number or an irrational number like pi or the square root of 3. An irrational number cannot be written as a fraction or have a decimal that is repeating or terminating.

Real Numbers

Together the rational and the irrational numbers are in the real numbers. Just like Osaka and Tokyo are both in Japan.

You have seen the organization of our Number System is structured much like all of the countires and cities we live in. And also Hayato in Japan learns this. Because the Number system is the same all over the world.

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