# How to distinguish between a rational number and an irrational number.

Explain how to distinguish between a rational number and an irrational number.

Numbers can be divided into natural numbers, whole numbers, integers, real numbers or complex numbers. Real numbers are further divided into rational numbers and irrational numbers.

Rational numbers:

• A number is said to be rational if it can be written in the form of a fraction such as p/q where both p (numerator) and q (denominator) are integers and denominator is a natural number (a non-zero number).

• Integers, fractions including mixed fraction, recurring decimals, finite decimals, etc., are all rational numbers

• Rational Numbers are either finite or are recurring in nature.

Examples:

Can be perfect squares such as 4, 9, 16, 25, 36, 49, and so on.

Or 3/2 = 1.5, 3.6767 , 6, 9.31, 64, 0.66666, 3.25

Irrational numbers:

Irrational numbers are the numbers which are not possible to express as fractions. Irrational Numbers are non-terminating as well as non-repeating in nature.

• These cannot be written in fractional form. So no concept of numerator and denominator here.

Examples:

These include surds such as √2, √3, √5, √11, π(Pi), etc.