Enrich your knowledge with our informative blogs

# What does e mean in math? Lowercase ‘e’ is also known as Euler’s number named after the famous mathematician Leonhard Euler. This number is an irrational number because it has a non – recurring decimal that stretches to infinity. Euler’s number ‘e’ is a numerical constant just like pi $(\pi )$ and is one of the key pillars in mathematical calculations.

The value of e is 2.71828182845…………

As e is an irrational number, it is usually used under logarithm concepts. e plays a key role in problem solving in both mathematics as well as physics. The symbol e is also known as Napier’s Constant.

The value of e raised to the power 1 will give the same value as e but value of e raised to the power 0 is equal to 1 and e raised to the power   gives the value as infinity. The reason is that e when results in a very big number or infinity. Similarly, when e is raised to negative power of infinity, the number turns out to be very small, which is almost equal to zero.

$\begin{array}{l}{{e}^{1}}\,\,=\,e\\{{e}^{0}}\,\,=\,1\\{{e}^{\infty }}\,=\,{{(2.71)}^{\infty }}\\{{e}^{{-\infty }}}=\,{{(2.71)}^{{-\infty }}}\,=0\end{array}$

Important things to note about e

• e is an irrational number i.e. digits after decimal are non-recurring. So, it cannot be expressed in the form of a fraction.
• e has its application in many areas, concepts and subjects such as advanced mathematics and physics.
• e is the base of all natural logarithms (This was discovered by John Napier).
• e is transcendental or non-algebraic. This means that e cannot be obtained by performing calculations of any non-zero polynomial having finite degree as well as rational coefficients.
• It’s the base to all natural logarithms i.e. Log (e) or Loge e = 1
• Area under the curve y = 1/x from x=1 to x=e is 1 sq. units.
• The slope of the graph of $y={{e}^{x}}$  lies between $y={{2}^{x}}$ and $y={{3}^{x}}$.

Euler’s number (e):

The Euler’s number ‘e’ is the limit of ${{(1+1/n)}^{n}}$ as n approaches infinity. It can also be expressed as the summation of the following series.

$e=\,\sum\nolimits_{{n=0}}^{\infty }{{}}1/n!$

e    = 1/0! + 1/1! + 1/2! + 1/3! + ………………….and so on  (here, ! means factorial)

e = 2.71828182845904523536028747135266249775724709369995…. which is an irrational number upto 50 decimal places.

Also, ${{e}^{x}}=1+\,\,\frac{x}{{1!}}\,+\,\,\frac{{{{x}^{2}}}}{{2!}}\,+\frac{{{{x}^{3}}}}{{3!}}\,+\,...,\,-\infty

e is also equal to $\underset{{x\to \infty }}{\mathop{{\lim }}}\,\,\left( {1+\frac{1}{n}} \right)n$  where n tends to infinity.

Let’s check the value of e for some numbers!

 n 1 2.00000 2 2.25000 5 2.48832 10 2.59374 100 2.70481 1,000 2.71692 10,000 2.71815 100,000 2.71827

For complex numbers the formula becomes:

eiπ + 1 = 0

This number is used in various mathematical concepts and calculations. Similarly, like other mathematical constants such as beta, gamma, pi etc the value of e plays an important role.

## Applications of e

Let’s check some areas where e plays a vital role not only in academics but in real life world as well.

• Compound Interest
• Probability, probability theorem, binomial distribution, binomial theorem and Pascal’s triangle.
• Standard Normal Distribution and Derangements
• Optical planning problems
• Asymptotics
• Differential and integral calculus
• Exponential and logarithmic functions ##### Unleash the Power of visualization to break tough concepts

Wanna be the next Maths wizard? Discover the new way of learning concepts with real-life Visualization techniques and instant doubt resolutions.

### Recent Posts  [footer-form]