Number Line and representation of various numbers on it!

In the previous post, you have seen there are various types of Numbers namely Natural Number, Rational Numbers, Irrational Numbers...etc. 
In order to understand, the meaning of each term we need know how to identify them and also how do they differ from one another. We shall be examining the Number line, posted below: 

Fig. 1.7 Real Numbers Line 

Natural Numbers: These are 

1, 2, 3, 4, 5, 6.................

Integers: You will notice there is a "0" zero  at the centre of the Number Line, there are Numbers with (+) sign on the right side and Numbers with (-) sign on the left, since these are Numbers with (+ve) or (-ve) signs attached these are known as Integers. The integers are written as;

....,-3, -2, -1, 0, 1, 2, 3,......

Rational Number: The rational numbers are expressed as ratios of Integers and are expressed as:

r = p/q

where p and q are integers and   q ≠ 0. The examples are:

   1/2      -3/5      35 = 35/1      0.15 = 15/100      etc.

Note: The division by 0 is not possible, as such ex[pressions such as  3/0  and 0/0 are undefined.

Irrational Numbers: There are also some Real Numbers such as √2, which cannot be expressed as a ratio of integers and are, therefore, called Irrational Numbers. It is possible to show that the following are also irrational numbers;

     √3      √5     ∛2      π       3/π²

Having decoded all the above issues let's go back to the Real Line. You can see that the Real Numbers can be represented by points on the Real Line, The positive direction (towards the right of the zero) is being indicated by the arrow. An arbitrary point, on the line, '0' is referred to as the Origin and it represents the real number "0". 

You can choose any unit of measurement..... every positive number, say x, is represented by the point (on the real line) at a distance of x-units to the right of the '0', similarly each negative integer -x is represented on the left of '0' as per its value. 

Having understood all the points above, you may have noticed that any Number associated with a value "P" can be referred to as co-ordinate of P and also the line can be called a coordinate line  OR a Real Number Line or in a more simple expression a Real Line. 

For all practical purposes one can identify the point with its coordinate and consider the number as a point on the Real Line.