Theory:

Suppose we want to locate the number \(5.6\)34¯ on the number line up to five decimal places.
 
That is, we have to represent \(5.6343434...\) on the following number line.
 
But it is as asked to represent up to \(5\) decimal places. Thus, we need to locate until \(5.63434\).
 
Let us consider the number line.
 
19.png
 
Now we will follow the procedure 'Process of successive magnification' to locate the number \(5.63434\).
 
Step 1: The range of the number \(5.63434\) is \(5\) and \(6\).
 
Step 2: Look for the range of the number on the number line and magnify that range (\(5-6\)) 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. That is,  \(5.6 -5.7\)
 
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. That is \(5.63-5.64\).
 
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 \(5.634 - 5.645\). Repeating the process of successive magnification, we need to magnify further \(5.6343 - 5.6344\). In this magnification, we can locate \(5.63434\).
 
35.png
 
Thus, we located the number \(5.63434\) on the number line by the process of successive magnification.