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Is A Number Real Calculator

Reviewed by Calculator Editorial Team

Determine whether a given number is real using our calculator. Learn about real numbers, their properties, and how to identify them in mathematical expressions.

What is a Real Number?

In mathematics, a real number is any number that can be found on the continuous number line. This includes all rational and irrational numbers, as well as integers, whole numbers, and natural numbers.

Real Number Definition: A number that can be expressed as a decimal (either terminating or repeating) and can be plotted on the number line.

Real numbers are distinct from complex numbers, which have an imaginary component. The set of real numbers is denoted by the symbol ℝ.

Properties of Real Numbers

  • Can be positive, negative, or zero
  • Can be whole numbers, fractions, or irrational numbers
  • Can be expressed as a decimal
  • Can be compared using the standard order relations

How to Check if a Number is Real

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

  1. Identify if the number has an imaginary component (i)
  2. Check if the number can be expressed as a decimal
  3. Verify if the number can be plotted on the number line

Note: All numbers without an imaginary component are real numbers. Numbers with an imaginary component (like 3 + 2i) are complex numbers and not real.

Mathematical Representation

A number is real if it can be written in the form a + bi, where b = 0. In this case, the number simplifies to a, which is a real number.

Examples of Real Numbers

Here are some examples of real numbers:

  • 5 (integer)
  • -3.7 (decimal)
  • 2/3 (fraction)
  • √2 (irrational number)
  • π (irrational number)

Non-Real Number Example

The number 4 + 3i is not a real number because it contains an imaginary component (3i).

FAQ

What is the difference between real and complex numbers?

Real numbers are numbers that can be plotted on the number line and do not have an imaginary component. 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 expressed as decimals and plotted on the number line.

Can a number be both real and imaginary?

No, a number cannot be both real and imaginary. A number is either real (no imaginary component) or imaginary (has an imaginary component).

What is the symbol for the set of real numbers?

The set of real numbers is denoted by the symbol ℝ.