Real Numbers Definition | Real Numbers Examples

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Real Numbers

Real numbers definition can be both positive or negative numbers which can be represented on the number line. They are the union of both rational and irrational numbers. It also includes whole numbers, natural numbers, all integers, and fractions. For example 23, -14, 7.87, 4/3, and so on.

Examples of Real Numbers

While it is fairly simple to recognize familiar numbers such as natural numbers and integers as real numbers, many people have questions about specific numbers. Zero is a genuine number. Real numbers include pi, Euler’s number, and phi. Real numbers include all fractions and decimal numbers.

Non-real numbers are either imaginary (for example, -1, i, 3i) or complex (a + bi). As a result, some algebraic expressions are real [for example, 2, -3, (1+ 5)/2] while others are not [for example, i2, (x + 1)2 = -9].

Properties of real numbers

There are four main properties of real numbers:

  • Commutative Property: For addition a+b=b+a and For multiplication axb=bxa
  • Associative Property: For addition a+(b+c)=(a+b)+c and For multiplication ax(bxc)=(axb)xc
  • Distributive Property: ax(b+c)=ab+ac and (a+c)xb=ab+cb
  • Identity Property: additive identity a+0=a and multiplicative identity ax1=a

If we add, subtract, multiply, or divide (except by zero) two rational numbers, we still get a rational number. However, the sum, difference, quotient, and product of irrational numbers are not always irrational.

Types of real numbers

  • Natural numbers
  • Whole numbers
  • Integers
  • Rational Numbers
  • Irrational Numbers

Venn Diagram


FAQ : Real Numbers

Q1: . Is pi a real number?

Ans: Because Pi cannot be expressed as a simple fraction, it is an irrational number. Every irrational number is a real number, we know. Pi is thus a real number.

Q2: Is √1 is a real number?

Ans: Yes, √1 is a real number

Q3: What are non-real numbers?

Ans: Non-real or non-imaginary numbers are those that are not real or imaginary. Non-real numbers cannot be represented on the number line.

Q4: How many types of real numbers?

Ans: There are five types of real numbers –  rational, irrational, integer, whole, and natural numbers.

After understanding real numbers definition, if you want to know Rational and Irrational Numbers, then check this article – Rational Numbers

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