The document discusses the number e. It is called the natural base of logarithms and gets its symbol e from its discoverer Leonhard Euler. Like pi, e is an irrational number. As n increases, 1+1/n to the nth power approaches e. Simplifying expressions with e works the same as with variables.

1. Algebra 2<br />8.3The Number e<br />The history of mathematics is marked by the discovery of special numbers. It all began with the “counting numbers,” when the cavemen counted how many sticks to put on a fire. Next came the idea of “zero.” Initially, zero was just a placeholder (like the 0 after “1” to represent “10”). Eventually it became the symbol for “nothing,” but this took a long time—the Greeks couldn’t understand 0 to be a number (how can nothing be something?) The idea of 0 as a number came about the same time in history as the discovery of negative numbers. The number π (pi) was known and used by the ancient Babylonians. It represents the ratio of the circumference of a circle to its diameter. Eventually, as math progressed, the real numbers were expanded into complex numbers with the discovery of the number i (which everyone loves!). Finally, we have one of the most famous numbers of the modern era: e.<br />The number e is called the _______________________________________________. It gets the symbol e from its discoverer ____________________________________________ (which is why it is sometimes called Euler’s number).<br />e, like π, is an ________________________________________ number.<br />n1011021031041051061+1nn2.594<br />As n increases, what happens to 1+1nn?<br />When n reaches _____________________________________, 1+1nn=e.<br />Simplifying expressions with e works just like with variables.<br />EX:<br />a. e3∙e4b. 10e35e2c. 3e-4x2<br />HW p. 483 (23 – 28, 49 – 52, 67 – 70 all)<br />