The number of form P/ q where p and q are integers and q not equal to zero is called rational number. Examples:-1/5,9/6,2/8 etc.

Rational numbers are those numbers that can be expressed as a fraction of two integers. These numbers can be represented in the form of p/q, where p and q are integers and q ≠ 0. Rational numbers can be either positive or negative.

Examples:

• 5/3


• -3/7


• 1/2


• 10/1

Irrational numbers are those numbers that cannot be expressed as a fraction of two integers. These numbers cannot be written in the form of p/q. They are non-repeating and non-terminating decimals. Irrational numbers can also be either positive or negative.

Examples:

• π (pi) = 3.1415926...


• √2 = 1.41421356...


• √3 = 1.7320508...


• e = 2.7182818...

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot. Rational numbers always have a finite or repeating decimal representation, whereas irrational numbers always have a non-repeating and non-terminating decimal representation.

Example:

• 5/2 = 2.5 (rational)


• √2 = 1.41421356... (irrational)

Real numbers are those numbers that can be represented on a number line. This includes both rational and irrational numbers. Real numbers can be either positive or negative and can include zero.

Example:

• -5 (rational and real)


• π (irrational and real)


• 0 (rational and real)


• 3/4 (rational and real)

In summary, rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot. Both rational and irrational numbers are included in the set of real numbers. Understanding the difference between these two types of numbers is important in mathematics and many other fields.