Theory:

The numbers with more decimal expansions (like \(1.278\), \(3.4218\),...) cannot be located directly on the number line.
 
To resolve this issue, we are going to learn the concept called 'Successive magnification'.
The process of visualisation of representation of numbers on the number line through a magnifying glass is called the process of successive magnification.
Procedure for the process of successive magnification:
 
Step 1: Locate the range of number.[nearest smallest and largest integers]
 
Step 2: Look for the range of the number on the number line and magnify that range alone. That is, divide the portion into \(10\) parts.
 
Step 3: Now let us look for the number with the first decimal point on the number line and find the range of that.
 
Step 4: Again magnify the range and divide the portion into \(10\) parts.
 
Step 5: Now look for the number with two decimal point on the number line.
 
Step 6: Repeat the process until you locate the entire decimals on the number line.
Example:
Suppose we want to locate the number \(1.257\) on the number line.
 
That is, we have to represent \(1.257\) on the following number line.
 
2.PNG
 
Step 1: The range of the number \(1.257\) is \(1\) and \(2\).
 
Step 2: Look for the range of the number on the number line and magnify that range alone. That is, divide the portion into \(10\) parts.
 
2_1.png
 
Step 3: Now let us look for the number with the first decimal point on the number line and find the range of that.
 
3_2.png
 
Step 4: Again magnify the range and divide the portion into \(10\) parts. Now look for the number with two decimal point on the number line.
 
4.PNG
 
Step 5: Again magnify the range and divide the portion into \(10\) parts. Now look for the number with three decimal point on the number line.
 
5.png
 
Thus, we located the number \(1.257\) on the number line by the process of successive magnification.