What is the difference between a rational and irrational number?

Rational numbers are the numbers which are integers and fractions

Irrational numbers are the numbers whose expression as a fraction is not possible

Examples of Rational Number

1/9 – Both numerator and denominator are integers.

7 – Can be expressed as 7/1, wherein 7 is the quotient of integers 7 and 1.

√16 – As the square root can be simplified to 4, which is the quotient of fraction 4/1

0.5 – Can be written as 5/10 or 1/2 and all terminating decimals are rational.

0.3333333333 – All recurring decimals are rational.

Examples of Irrational Number

√2 – √2 cannot be simplified and so, it is irrational.

√7/5 – The given number is a fraction, but it is not the only criteria to be called as the rational number. Both numerator and denominator need to integers and √7 is not an integer. Hence, the given number is irrational.

3/0 – Fraction with denominator zero, is irrational.

π – As the decimal value of π is never-ending, never-repeating and never shows any pattern. Therefore, the value of pi is not exactly equal to any fraction. The number 22/7 is just and approximation.

0.3131131113 – The decimals are neither terminating nor recurring. So it cannot be expressed as a quotient of a fraction.

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