What are the Different Types of Numbers?

Numbers form the basis of Mathematics. There are many types of numbers that make up a part of the number system that kids have to know about. In this article, we will learn about various kinds of numbers, such as whole numbers, irrational numbers, natural numbers, etc., and their associated properties.

Natural Numbers

These are known as the counting numbers and consist of all numbers excluding 0. Thus we can say 1, 2, 3, 4 …. are natural numbers.

Properties of Natural Numbers

• The addition and multiplication of any natural number are associative and commutative.
• One is known as the multiplicative identity of a natural number while 0 is the identity element for addition.

Whole Numbers

Counting numbers that start with 0 are known as whole numbers. These numbers do not contain any negative number, decimal, or fractional part. Thus, 0, 1, 2, 3 …. are whole numbers.

Properties of Whole Numbers

• Whole numbers are commutative and associative under addition and multiplication.
• 1 is the multiplicative identity meaning that any number except 0 that is multiplied by 1 gives the number itself.
• It obeys the distributive property of multiplication over addition and subtraction.
• If a number is added to 0, it gives the number itself, making 0 the additive identity.

Rational Numbers

A number that can be expressed in the form of p/q or as a ratio is known as a rational number. The decimal expansion of a rational number can be terminating or non-terminating and repeating. Examples are 8/9, 7/4, 5/1, etc.

• Rational numbers satisfy the commutative and associative property under addition and multiplication.
• They are also closed under division, subtraction, multiplication, and addition.
• The distributive property is obeyed for subtraction and addition with multiplication.

Integers

It consists of the set of whole numbers and negative numbers. Thus, … -2, -1, 0, 1, 2 … are integers.

Properties of Integers

• The addition and Multiplication of integers are commutative and associative.
• They are closed under multiplication, addition, and subtraction.
• The multiplicative identity of integers is 1, while additive identity is 0.

Real Numbers

All types of numbers that are not imaginary fall under real numbers. They include positive, negative integers, fractional, or decimal numbers. Thus, 5.4, 5/4,√2, -7, 69, etc., are real numbers.

Properties of Real Numbers

• The addition and multiplication of real numbers are associative, commutative, and distributive.
• The inverse property is obeyed
• 0 and 1 are additive and multiplicative identities, respectively.

Irrational Numbers

Any number that cannot be expressed in the form of p/q is known as an irrational number. They have non-repeating and non-terminating decimal expansions.√5, pi, etc., are examples of these numbers.

Properties of Irrational Numbers

• Closure property is not satisfied by irrational numbers.
• Addition and multiplication obey the associative and commutative properties.
• They can distribute under addition and subtraction with multiplication.

Complex Numbers

A number that has a real part and an imaginary part that can be expressed in the form of a+bi is known as a complex number. a and b are real numbers, while i represents the imaginary part. Example 5 + 7i, -9 – 8i etc.

Conclusion

If a child wants to get a holistic understanding of numbers, then he should turn to an online educational platform such as Cuemath. At Cuemath, the math experts guide students through developing the best quality of knowledge that helps them throughout their lives.