### Theory:

Suppose we want to locate the number $$5.6$$$\overline{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 $$5.63434$$.

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 $$5.63434$$.

Thus, we located the number $$5.63434$$ on the number line by the process of successive magnification.