Rational Numbers & Irrational Numbers | Examples

Rational Numbers

The numbers of the form a/b, where a and b are integers and b ≠ 0 are known as rational numbers.

Example: 1/2, -4/5, 0, -1, 2 etc.

or

A number which can be expressed as a terminating decimal or repeating decimal, is called a rational numbers.

Example: 5/3 = 1.666666....... = 1.6
              16/45 = 0.355555 ...... = 0.35 etc.

Important result

all natural numbers, whole numbers and integers are rational numbers.

We can understand above terms with a picture diagram.

Irrational Numbers

A number which can neither be expressed as a terminating decimal nor a repeating decimal, is called an irrational number.

Thus, non-terminating, non-repeating decimals are irrational numbers.

Examples:

Type 1. 0.2020020002....... , 0.4040040004...... etc. are a non-terminating and non-repeating decimal, therefore these are irrational number.

Type 2: If n is positive which is not a perfect square, then √n is irrational, e.g. √2, √3, √5, √6, √7, √8, √10, √11 etc.

Type 3: If n is positive which is not a perfect cube, then ³√n is irrational, e.g. ³√2, ³√3, ³√4, ³√5, ³√6, ³√7, ³√9, ³√10 etc.

Important Result

𝛑 is irrational, while 22/7 is rational number.