The Real Number System 101

Updated: Jan 5

Hello everybody! Today we will be talking about the real number system. The real number system consists of six different types of numbers including real numbers, rational numbers, irrational numbers, non-integer fractions, integers, negative numbers, whole numbers, zero, and natural numbers. Today we will only be talking about whole numbers, integers, and rational numbers. I hope you enjoy!

What is a whole number? A whole number is all positive numbers including zero. But all whole numbers cannot be fractions and decimals and can only be whole, as in there aren’t any missing pieces. For example, ¾ has ¼ missing from it, so it is not a whole number. Whole numbers are 0, 1, 2, 3, 4, 5, 6, and so on. Whole numbers cannot be negatives as well. So in order for a number to be a whole number, it cannot be a fraction, decimal or whole number.

What is an integer? An integer is a whole number either positive or negative. Another definition is all whole numbers and the opposites of all of the whole numbers. Integers cannot be fractions or decimals but can only be whole numbers or the negatives of whole numbers. Do not confuse whole numbers and integers, however, whole numbers are similar to integers since they cannot be fractions or decimals, but integers can be negative unlike whole numbers. Integers are very not only just a type of number, but are important to understand in order to understand other types of numbers such as rational numbers!

So what is a rational number? A rational number is a number that can be put into this format p/q as in a fraction. Now don’t get too confused...p and q are only just placeholders for integers which is what I explained in the first paragraph. And q cannot be equal to zero. For example, 3 is a rational number because it can be put into this format. Like this: 12/6 is equal to 3 and q (which is the 6) is not equal to zero so we’re good! What is an example of a non rational number? A well known example of a number that isn’t a rational number is π. Which is needed to calculate the circumference of a circle. π is a number that keeps on going and never stops. The beginning is: 3.1415926535, but keeps on going. π cannot be put into the p/q format where q cannot equal zero. This is because it keeps going. π is close to 22/7 but is not equal to 22/7. So, if a number is a rational number, you can put it in a p/q format where p and q are both integers (explained above) and q is not equal to zero.

Thank you for reading about the real number system! In my next post two posts about the real number system I will cover real numbers, irrational numbers, non-integer fractions, negative numbers, zero, and natural numbers. We all know about numbers, but as you dive deeper into math, you start to learn more about the different types of numbers and how numbers can be different from each other in different ways! I hope you enjoyed reading about the real number system! I hope you enjoyed reading!

Question #1: What is a whole number?

  1. A number that is not a fraction, decimal, or negative

  2. A number that ate a whole meal

  3. A big number

  4. A small number

Question #2: What is an integer

  1. Whole numbers, and negative whole numbers

  2. When you make an inference about something

  3. When a number is shaped like an imp

  4. When a number is small

Question #3: What is a rational number?

  1. A rational number can be be put in a p/q format where p and q are integers and q ≠ 0

  2. A rational number is a number that has common sense

  3. A rational number is a very smart number

  4. A rational number is a number that is a critical thinker


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