Real or Not Real Number Calculator

A real number is any number that can be found on the number line. This includes all rational and irrational numbers. Our real or not real number calculator helps you determine whether a given number is real by analyzing its properties.

What is a Real Number?

In mathematics, a real number is defined as any value that can be represented on the number line. Real numbers include all rational numbers (fractions, integers, decimals) and irrational numbers (non-repeating, non-terminating decimals).

Real numbers can be positive, negative, or zero. They can also be whole numbers or have fractional parts. The set of real numbers is often denoted by the symbol ℝ.

Real numbers are distinct from complex numbers, which include an imaginary component (e.g., 3 + 4i). Complex numbers cannot be plotted on the standard number line.

How to Check if a Number is Real

To determine if a number is real, follow these steps:

Check if the number can be expressed as a fraction or decimal.
Verify that the number does not contain an imaginary unit (i).
Ensure the number is not infinite or undefined.

If a number meets these criteria, it is real. If it contains an imaginary component or is infinite/undefined, it is not real.

For a number z to be real:

Im(z) = 0

Where Im(z) is the imaginary part of the number.

Examples of Real and Non-Real Numbers

Here are some examples to illustrate real and non-real numbers:

Number	Type	Explanation
5	Real	An integer on the number line
3.14159	Real	A decimal approximation of π
√2	Real	An irrational number
2 + 3i	Not Real	Contains an imaginary component
∞	Not Real	Infinite, not a finite value

Frequently Asked Questions

What is the difference between real and complex numbers?

Real numbers can be plotted on the number line and include all rational and irrational numbers. Complex numbers include an imaginary component (i) and cannot be plotted on the standard number line.

Are all integers real numbers?

Yes, all integers are real numbers because they can be found on the number line and do not contain an imaginary component.

Can a number be both real and irrational?

Yes, numbers like √2 and π are both real and irrational because they cannot be expressed as simple fractions and can be plotted on the number line.