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

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

awitiotiz Answered question September 19, 2022

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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.

awitiotiz Answered question September 19, 2022