Value of e


Basically, it is a logarithm concept. Also, the value of e is a mathematical constant that is basically the base of the natural logarithm. Moreover, it is important not only in math but also for other subjects like physics. However, the value of e is 2.71828182… so on. Furthermore, if the value of e to the power 1 \((e^{1})\) will give the same value as e however the value of e to the power 0 \((e^{0})\) is equal to 1 and if e rises to the power infinity then it gives the value as 0. Besides, this is a unique and special number, whose logarithm gives the value as 1, which is Log e = 1.

Euler’s Number

We know the letter ‘e’ Euler’s Number because Swiss mathematician Leonhard Euler used this particular letter to represent this mathematical constant and it is named after him. Furthermore, it is the limit of \((1 + 1/n)^{n}\) as n approaches infinity, an expression that arises in the study of compound interest. Moreover, we can express it as the sum of infinity numbers.

\( e = \sum_{n=0}^{\infty } \frac{1}{n!} = \frac{1}{1} + \frac{1}{1} + \frac{1}{1.2} + \frac{1}{1.2.3} …..\)n

We can calculate the value of e by solving the above equation. In addition, this will result in an irrational number that we can use in various mathematical concepts and calculations. Moreover, we also know the Euler Number as Napier’s constant, which Jacob Bernoulli discovered while studying the compound interest.

Also, like other mathematical constants such as ß, π, γ, etc. the assessment of constant e also shows a significant role. In addition, the number e has similar properties just like other numbers. Moreover, we can operate all the mathematical operations using the value of e (logarithm base value of e).

What is the value of e in Maths?

The expression for Euler Number gives the sum of infinite for the Euler’s constant e, which we can express as:

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

Hence, the value of \(( 1 + 1/ n)^{n}\) reaches e when n reaches ∞. Moreover, if we put the value of n in the above expression then we can calculate the approximate value of number e. Thus, let’s start putting the value of n = 1 to higher digits.

Value of n Putting value of n in \( (1 + 1/n)^{n}\) Value of constant e
1 \( (1 + 1/1)^{1}\) 2.00000
2 \( (1 + 1/2)^{2}\) 2.25000
5 \( (1 + 1/5)^{5}\) 2.48832
10 \( (1 + 1/10)^{10}\) 2.59374
100 \( (1 + 1/100)^{100}\) 2.70481
1000 \( (1 + 1/1000)^{1000}\) 2.71692
10000 \( (1 + 1/10000)^{10000}\) 2.71815
100000 \( (1 + 1/100000)^{100000}\) 2.71827

Value of Exponential Constant

It is a significant mathematical constant and we can denote it by symbol ‘e’. Moreover, it has an approximate value equal to 2.718.  Furthermore, we frequently use to model physical and economic phenomena, mathematically, where it is convenient to write e. In addition, we can easily describe the exponential function using this constant. For example, \( y = e^{x}\) thus, when the value of x arises then we can calculate the value of y.

The Complete Value of e

The value of e or Euler Number is a very large number of digits. Moreover, we can count it up to the thousand-digit place. However, in mathematical calculations, we can only use the approximate value of e (Euler Number), equals to 2.72. Besides, the value of e to some number is as follows:

e = 2.718281828459045235360287471352662497757247093699959574966………..

Solved Example for You

Q1: What is the value of e to the power zero \( (e^{0}) \)?

A1:  If you raise any number to zero then it will only be one. Moreover, 0 is neither negative nor positive. So, when we raise e to the power zero then it will result in 1.

Share with friends
Customize your course in 30 seconds

Which class are you in?

Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
Ashhar Firdausi
IIT Roorkee
Dr. Nazma Shaik
Gaurav Tiwari
Get Started
Customize your course in 30 seconds

Which class are you in?

No thanks.