Number Line using Successive Magnification

We know that on a number line between any two points infinite number of point exist. So any number can be plotted on the number line by magnifying the line between two points,

Number Line using Successive Magnification:

To visualize the position (or representation) of numbers in decimal form the steps are

1. Analyse the given number and find the two points between which the number will lie.

2. Magnify the line between these two points.and find points with one decimal point between which the number will lie.

3. Repeat the step 2 for each decimal point.

This process of visualization of numbers on the number line, through a magnifying glass, is known as the process of successive magnification.

Illustration:  To visualize the representation of 5.28 on the number line.

Solution:We observe that 5.28 lies between 5 and 6. So, let us look closely at the position of the number line between 5 and 6.

We divide this portion into 10 equal parts and mark each point of division as shown in figure below This first mark to the right of 5 will represent 5.1, the second 5.2 and so on. To see this clearly, we magnify this portion by taking magnifying glass and look at the portion between 5 and 6. Through magnifying glass this portion between 5 and 6. As. 5.28 lies between 5.2 and 5.3. So, let us mark 5.2 and 5.3 and magnify the portion between them

We will again divide this portion into 10 equal parts and mark each point of division as shown in figure below This first mark to the right of 5.2 will represent 5.21, the second 5.22 and so on. To see this clearly, we magnify this portion by taking magnifying glass and look at the portion between 5.2 and 5.3 . The required point is 5.28

This process of visualization of numbers on the number line, through a magnifying glass, is known as the process of successive magnification.