In mathematics, an irrational number is any real number which cannot be expressed as a fraction a/b, where a and b are integers, with b non-zero, and is therefore not a rational number. Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are precisely those real numbers that cannot be represented as terminating or repeating decimals. The best-known irrational numbers are π, e and √2.

The number  is irrational.

The real line

In mathematics, the real line, or real number line is the line whose points are the real numbers. That is, the real line is the set R of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one.

Just like the set of real numbers, the real line is usually denoted by the symbol R (or alternatively, the letter �R� in blackboard bold). However, it is sometimes denoted R in order to emphasize its role as the first Euclidean space.

http://en.wikipedia.org/wiki/Real_line

The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.

(Our solved example in mathguru.com uses the below concept. This is our own explanation and has not been taken from Wikipedia.)

To represent (say) on number line

Steps of Construction

(1) Mark the distance x units from a fixed point A and obtain a

point B such that AB = x units.

(2) From B, mark a distance of 1 unit and mark the new point as

C.

(3) Find the midpoint of AC and name it as M.

(4) Taking MC as the radius, draw a semi circle.

(5) Draw a line perpendicular to AC passing through B and

intersecting the semi circle at D.

(6) Draw an arc with Center B and radius BD, which intersects

the number line in E.

(7) Then, E represents.