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Home Education

What are Real Numbers? Properties and Types of Real Numbers

mindmingles by mindmingles
1 year ago
in Education
Reading Time: 3min read
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Article Summury

    • History
    • Types of Real Numbers
    • Irrational Numbers
    • Rational Numbers 
    • Fractions
    • Integers
    • Negative Numbers
    • Whole Numbers
    • Natural Numbers
    • Properties of Real Numbers
    • Commutative Property
    • Associative Property
    • Distributive Property
    • Identity Property
    • Conclusion
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A value that represents a quantity along a continuous number line is called a real number. They are a combination of rational numbers and irrational numbers. Integers, natural numbers, negative numbers, whole numbers, etc., are real numbers. Imaginary numbers cannot be represented on a number line, and therefore, they do not fall under the types of real numbers.

History

Around 1000 BC, simple fractions were used by Egyptians. Early Indian Mathematicians such as Manava (750 – 690 BC) accepted the concept of irrationality. They found that square roots of certain numbers such as 2 could not be determined precisely. The importance of the square root of 2 was also realized by Greek Mathematicians led by Pythagoras. 

 

Indian and Chinese Mathematicians accepted concepts of zero, negative numbers, fractional numbers, and integers during the middle ages. Arabic Mathematicians eventually merged all these numbers into one topic called real numbers. As research progressed further, the concept of real numbers developed into what we know them as today. 

Types of Real Numbers

Real numbers can be classified as follows:

Irrational Numbers

Numbers that cannot be written in the form of p/q and are not rational numbers are called irrational numbers. They are non-terminating and non-repeating. An example of an irrational number is 2.

Rational Numbers 

Numbers that can be expressed in the form of p/q wherein q is not equal to 0. Rational numbers can be positive or negative. They are terminating or non-terminating and repeating decimals. Examples are 0.3333, 0.25 etc.

Fractions

Fractions fall under the category of rational numbers. All fractional numbers are rational numbers, but all rational numbers are not fractions. A fraction is any number that can be expressed in the form a/b where a and b are whole numbers, and b is not equal to 0.

Integers

Integers also fall under the category of rational numbers. Whole numbers and all negative natural numbers make up integers.

Negative Numbers

Numbers that are below zero are called negative numbers. They fall under the category of integers.

Whole Numbers

These numbers also fall under the category of integers and consist of all-natural numbers and zero.

Natural Numbers

All counting numbers that start from one are called natural numbers. 

Properties of Real Numbers

The properties of real numbers are as follows

Commutative Property

The numbers can be moved from their position without changing the final answer. This property can be applied to addition and multiplication. If a and b are two numbers then according to this property a+b = b+a and a.b = b.a

Associative Property

Regardless of the grouping of numbers, you can add and multiply them without altering the result. If we have three numbers a,b,c then according to this property a+(b+c) = (a+b)+c and a.(b.c) = (a.b).c

Distributive Property

If you multiply the sum of two or more numbers, the result should be the same as multiplying each number individually by the said number and adding their sum. Let a,b,c be three numbers then a.(b+c) = a.b+a.c 

Identity Property

If a number is multiplied by 1, you get the same number, i.e., a.1=a. Also, if zero is added to the number, it stays the same. a + 0 = a. This is the identity property.

Conclusion

If you want to have a clear foundation about the types of real numbers, Cuemath is the place to go. It is an online educational platform that combines fun with learning to provide quality education to a child.

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