# Euler's Number

Euler's Number

In mathematics, we deal with several terminologies with fixed numeric values. These are called constants, and they help in solving mathematical problems with ease.

For example, $$\pi =3.14$$

Likewise, there is a constant e, known as Euler’s number. It was discovered in the 18th century. It is quite interesting to learn about the history of Euler’s number. It is the base of the natural logarithm. The

In math, the term e is called Euler's number after the Swiss mathematician Leonhard Euler.

It is mathematically known as Euler's (pronounced as oiler) constant or Napier's constant.

In this chapter, you will learn about

• Euler's number value
• How to calculate e without using Euler's number calculator
• Euler's number proof
• Euler's number digit

## Lesson Plan

 1 What is Euler's Number? 2 Important Notes on Euler's Number 3 Solved Examples on Euler's Number 4 Thinking out of Box! 5 Interactive Questions on Euler's Number

## What is Euler's Number?

Euler's number (e) play's a crucial role in mathematics. It represents the basis of the exponential functions and logarithms. Euler's number digit are$e = 2.717281728459045$ The value of e is approximately equal to $e = 2.718$

The number was first coined by Swiss mathematician Leonhard Euler in the 1720s. John Napier, the inventor of logarithms, made significant contributions to developing the number, while Sebastian Wedeniwski calculated it to 869,894,101 decimal places.

$$e$$ is called the Euler Number, the Eulerian number, or Napier's Constant. Euler's number proof was first given as that $$e$$ is an irrational number, so its decimal expansion never terminates.

This mathematical constant is not only used in math but equally important and applicable in physics.

## General Formula of Euler's Number

$$e$$ is mathematically represented and defined by the following equation:

 \begin{align} e=\lim_{n\rightarrow\infty}\left( 1+\frac{1}{n}\right)^n\end{align}

Let us have some practical experience of putting the value n to calculate the value of Euler's number digit:

### Value of e

1 $\ e_1=\left( 1+\frac{1}{1}\right)^{1}$

2.00000

2 $\ e_2=\left( 1+\frac{1}{2}\right)^{2}$

2.25000

5 $\ e_5=\left( 1+\frac{1}{5}\right)^{5}$

2.48832

10 $\ e_{10}=\left( 1+\frac{1}{10}\right)^{10}$

2.59374

100 $\ e_{100}=\left( 1+\frac{1}{100}\right)^{100}$

2.70481

1000 $\ e_{1000}=\left( 1+\frac{1}{1000}\right)^{1000}$

2.71693

10000 $\ e_{10000}=\left( 1+\frac{1}{10000}\right)^{10000}$

2.71815

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus
Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school