Question

2. How do we recognise them? That is, how do we
distinguish them from the rationals (rational
numbers)?​

Answer 1

The difference between rational and irrational numbers is as follows:

• Rational and irrational numbers are the complex form of representation of number in Mathematics.  
• A number which can be expressed in the form of a ratio of two integers is a rational number whereas an irrational number has endless non-repeating digits.  
• The rational numbers include perfect squares whereas the irrational numbers include surds.
• Decimal expansion in case of the rational numbers is finite or recurring decimals.
• In case of the irrational numbers, the decimal expansion is non-finite or non-recurring decimals.
• The example of a rational number is 1/2 and of irrational is π = 3.141.