What Are Real Numbers?
What are Real Numbers in Math? - Definition and Examples
Understanding what are real numbers in math is an important foundation skill that every student must learn. This page includes everything you need to know about real numbers, including the definition of a real numbers, examples (and non-examples) of real numbers, and a visual representation of real numbers using the number line.
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What are real numbers? Explained.
What are Real Numbers? - Definition
So, what is a real number in math?
Definition: A real number is any number that can be plotted on the number line.
Real numbers can be:
✅ whole numbers (e.g. 8, 3,496)
✅ negative numbers (e.g. -12, -7,000,000)
✅ factions (e.g. 2/3, -9/7)
✅ decimals (e.g. 0.125, -44.4)
✅ rational numbers (e.g. 0.333, 9/10)
✅ irrational numbers (e.g. π, √(3))
Real numbers cannot be:
❌ imaginary numbers (e.g. √(-1) or 9i)
❌ complex numbers (e.g. 3 + 4i)
❌ concepts representing quantities (e.g. ∞)
What is a Real Number? - Examples
In fact, almost any number, big or small, that you could every imagine is a real number.
As long as a number is not imaginary or complex, then it is a real number. Numbers that fall into this category are called “Real” because they are not imaginary.
The graphic in Figure 01 shows a few more examples of real numbers, all of which can be plotted somewhere on the number line. And, by definition, if a value can be plotted on the number line, then it is a real number.
These examples of real numbers include 7, 2.5. -5.75. 4/5, √5, and π. While these numbers may all seem very different from each other, they can all be plotting on the number line, meaning that they are all real numbers.
Figure 01: What are real numbers? A real number is any number that can be plotted on the number line.
Real Numbers on the Number Line
If you are still confused about what are real numbers, it can be super helpful to take a closer look at the number line.
The number line (which is sometimes referred to as the real number line) is a horizontal line with an origin point at zero that extends forever in a positive direction (→) and forever in a negative direction (←). This relationship is illustrated in Figure 02 below.
Given that the real number line includes pretty much any number, big or small, that you or anyone else could ever think of, it should make sense that almost every number is a real number.
So, if you are ever unsure of whether or not a number is a real number, simply ask yourself if the number could be plotted anywhere on a number line. If the answer is yes, then the number is a real number.
In short, any value that can be found on the number line is a real number (for example: 29, 11/7, and π). However, since imaginary numbers (like √(-2) or 2i), complex numbers (like 3 + 4i), and concepts like infinity (∞) can not be plotted on the number line, they are not real numbers.
Figure 02: What are real numbers? Any number that can be plotted on a number line is a real number.
Is 0 a Real Number?
Before we wrap up our exploration of what real numbers in math, let’s answer take a look at one extremely common question: is 0 a real number?
To answer the question, is zero a real number?, we have to see if 0 is, by definition, a true real number.
Remember that, in math, a real number is any number that can be plotted on the number line.
So, can zero be plotted on the number line? Absolutely, yes!
In fact, 0 is the “origin” of the real number line. And, since zero can be plotted on the number line, we can conclude that zero is a real number.
Answer: Is 0 a real number? YES.
The graphic in Figure 03 below shows where zero falls on the number line and why 0 is a real number.
Figure 03: Is 0 a real number? Yes!
Free Blank Number Lines for Students
Could you use a free collection of printable blank number lines? Whether you are a math student, a classroom teacher, or a parent looking to help your kids at home, our free blank number lines are an awesome tool that can help young learners to practice and learn a variety of math topics and skills.
