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The Real Number System 102

Updated: Aug 7, 2021

Hello! Today I will be talking more about the real number system, specifically about three different types of numbers...irrational numbers, real numbers, and non-integer fractions! The real number system is made up of nine different types of numbers including real numbers, rational numbers, irrational numbers, non-integer fractions, integers, negative numbers, whole numbers, zero, and natural numbers. Check out my last post where I talked about whole numbers, integers, and rational numbers! I hope you enjoy!

What is an irrational number? An irrational number is a non-repeating and non-terminating decimal. So what does non-repeating and non-terminating mean? A non-repeating decimal means that no number repeats endlessly. An example of a non-repeating decimal is ⅓ because the decimal for it is 0.33333333 and the three’s keep going endlessly. This would not be considered a non-repeating decimal. A non-terminating is a decimal that never stops going. ⅓ would be considered a non-terminating decimal because it never ends and it keeps going. But in order for a number to be considered an irrational number it has to meet both qualifications so even though ⅓ is considered a non-terminating, it isn’t a non-repeating decimal. An example of an irrational number is 𝛑. Pi is needed to make the calculation of the circumference of a circle. Pi is a number that keeps going and going and never stops. This qualifies it as a non-terminating decimal. Pi also doesn’t ever start repeating the same number at a point and keep going with the number qualifying it as a non-repeating decimal. So an irrational number is a number that is a non-repeating and non-terminating decimal.

How do you know if a number is a real number? A real number is quite simple to understand and is either an irrational number or rational number. The real number system is called the real number system for a reason. Real numbers are basically the umbrella for the entire real number system. This is because pretty much every number is a real number. The real number system starts with real numbers and branches off into rational numbers and irrational numbers since those are what make up rational numbers. And below rational numbers it branches off to non-integer fractions and integers. Branching off of integers you come to negative numbers, and whole numbers. After whole numbers you finally conclude to zero, and natural numbers. At the end of my third post I hope you understand all the components of the real number system and why they are structured the way they are.

What is a non-integer fraction? A fraction is considered a non-integer fraction if the numerator is not a multiple of the denominator. By saying that the numerator cannot be a multiple of the denominator means that if the denominator were to be multiplied by any number it would never equal the numerator. Examples of a non-integer fraction include ½, 5/4, and 3/7.

Thank you for reading my second post on the rational number system! Today we covered what an irrational number is, what a real number is, and non-integer fractions! I also talked about why the real number system is called the real number system and how it was structured! I hope you enjoyed reading! Make sure to read my next post on the last three sections of the rational number system!

Question #1: What is an irrational number?

  1. A number that is non-repeating and non-terminating