Is the number e rational or irrational?

Question

Sadie Ackerman · Accepted Answer

#e# is an irrational number.

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.

Chloe Alexander · Answer

undefined The number e, which is approximately 2.71828, is irrational. This means that it cannot be expressed as a ratio of two integers and its decimal representation neither terminates nor repeats. The number e is a fundamental mathematical constant that arises naturally in various mathematical contexts, particularly in calculus and exponential functions. Its irrationality was proven by Euler in the 18th century.