# Euler Number Or E Number: How Much It Is Worth, Properties, Applications

The **Euler number or number e** is a well-known mathematical constant that appears frequently in numerous scientific and economic applications, along with the number π and other important numbers in mathematics.

A scientific calculator returns the following value for the number e:

e = 2.718281828 …

But many more decimals are known, for example:

e = 2.71828182845904523536…

And modern computers have found trillions of decimal places for the number e.

It is an *irrational* number , which means that it has an infinite number of decimal places with no repeating pattern (the sequence 1828 appears twice at the beginning and is no longer repeated).

And it also means that the number e cannot be obtained as the quotient of two whole numbers.

**History**

The number *e* was identified by the scientist Jacques Bernoulli in 1683 when he was studying the problem of compound interest, but it had previously appeared indirectly in the works of the Scottish mathematician John Napier, who invented logarithms around 1618.

However, it was Leonhard Euler in 1727 who gave it the name number e and intensively studied its properties. That is why it is also known as the *Euler number* and also as a natural base for the natural logarithms (an exponent) currently used.

__How much is the number e worth?__

__How much is the number e worth?__

The number e is worth:

e = 2.71828182845904523536…

The ellipsis means that there are an infinite number of decimal places and in fact, with today’s computers, millions of them are known.

**Representations of the number e**

There are several ways to define e that we describe below:

**The number e as a limit**

One of the various ways in which the number e is expressed is the one that the scientist Bernoulli found in his works on compound interest:

In which you have to make the value *n* a very large number.

It is easy to check, with the help of a calculator, that when *n* is very large, the previous expression tends to the value of *e* given above.

Of course we can wonder how big *n* can be made , so let’s try round numbers, like these for example:

n = 1000; 10,000 or 100,000

In the first case, e = 2.7169239… is obtained. In the second e = 2.7181459… and in the third it is much closer to the value of *e* : 2.7182682. We can already imagine that with n = 1,000,000 or larger, the approximation will be even better.

In mathematical language, the procedure of making *n* get closer and closer to a very large value is called the *limit to infinity* and is denoted like this: