A rational number is one which can be expressed as a ratio of two integers.

When numbers are mentioned in decimal form, either rational limits to number of place after decimal or it has set or chain (in can be one or few digits as well) of numbers repeating endlessly such as #1.bar(3)333...# or #-7.4bar(25)2525.... or # or #13.63bar(285714)285714....#, in which cases set of numbers under the bar repeat themselves endlessly. There are ways by which such numbers can be expressed as ratios of two integers. For example first number is #4/3#, second number is #-7351/990# and third is #95742/700#.

#e# is number which cannot be written as ratio of two integers and when written in decimal form, no repeating pattern is observed. Hence, it is an irrational number.