Question

In mathematics, the irrational number \[e = 2.718...\] Which of the following letters corresponds to the number \[e\] on the number line below \[?\]

Answer 1

Hint: A set is a collection of objects, typically grouped within braces \[\{ \} \], where each object is called an element or digit. For example, {apple, mango, banana} is a set of fruits. A subset is a set consisting of elements that belong to a given set. For example, {apple} is a subset of the set above.

Complete step-by-step answer:
Irrational numbers are defined as any number that cannot be written as a ratio of two integers. Simply, non terminating decimals that do not repeat are irrational. For example, \[\pi = 3.14159...\] and \[\sqrt 2 = 1.41421...\]
We have to find the letter whose value is near or approximately equal to \[e\] in the number line. First find the value of each part in the given number line by dividing the difference between the value and the number of parts.
A number line allows us to visually display real numbers by associating them with unique points on a line. The real number associated with a point is called a coordinate. A point on the real number line that is associated with a coordinate is called its graph.
To construct a number line, draw a horizontal line with arrows on both ends to indicate that it continues without bound. Next, choose any point to represent the number zero; this point is called the origin. Mark off consistent lengths on both sides of the origin and label each tick mark to define the scale. Positive real numbers lie to the right of the origin and negative real numbers lie to the left. Typically, each tick represents one unit.

Since the part between \[2.7\] and \[2.75\] is divided into \[5\] parts. So, each part measures
 \[\dfrac{{2.75 - 2.7}}{5} = 0.01\].
 \[e = 2.718\] is to be located on the number line.
So, on analysis, we can say that point \[B\] is the correct point.
So, the correct answer is “Option B”.

Note: Note that the scale need not always be one unit. Also note that the number zero \[(0)\] is neither positive nor negative. A number line is also known as a real number line. The number \[e\] is the base of the Natural Logarithms.