Difference between rational and irrational numbers

Learn about rational and irrational numbers. Today In this topic am going to discuss the main points that will give idea about difference between rational and irrational numbers. Knowing about irrational and rational numbers is very important for middle class students.

Difference between rational and irrational numbers

From the names of the numbers (rational and irrational) we can now there is a slight difference between rational and irrational numbers. First, we will learn the definition of irrational numbers and also rational numbers. After learning definitions we will come to know the difference between rational and irrational numbers.

Definition of a rational number and examples:

All the numbers that can be expressed in x/y form where p and q should be integers, q is not equal to zero is called a rational numbers. These numbers ( rational ) represented by Q.

Examples:

-1, 0, -5/2, 7/-9,…..are rational numbers because all these are in the form of x/y.

Important properties of rational numbers:

All the natural numbers are rational numbers but all rational numbers need not be natural numbers.

All the whole numbers are rational numbers but all rational numbers need not be whole numbers.

All the integers are rational numbers but all rational numbers need not be integers.

All the rational numbers will be either terminating decimal or non terminating repeating decimal.

Definition of irrational numbers with examples:

All the numbers which cannot be expressed as x/y form is called an irrational numbers. These numbers (irrational) represented by QI.

Examples:

 √2, √3 , √5 , …….are irrational numbers.

Difference between rational and irrational numbers

The main which shows the Difference between rational and irrational numbers:

Rational Number

Irrational number

Can be expressed in x/y form Cannot be expressed in x/y form
Denoted by Q Denoted by QI
It is either terminating decimal or non-terminating repeating decimal It is non terminating non-repeating decimal
Rational numbers also includes all the perfect square numbers It contains only surds

 

The above-listed points are the main differences between irrational and rational numbers. So after reading all the above points, one can easily differentiate between rational and irrational numbers.

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