Question

Visualise the representation of 7.67 on the numberline through successive magnification upto three decimal places

Answer 1

Answer:

We locate 4.  

26

 on the number line, by the process of  

successive magnification. This has been illustrated in Figure.

Step 1: First we note that 4.  

26

 lies between 4 and 5

Step 2: Divide the portion between 4 and 5 into 10 equal  

parts and use a magnifying glass to visualise that 4.  

26

 lies  

between 4.2 and 4.3.

Step 3: Divide the portion between 4.2 and 4.3 into 10  

equal parts and use a magnifying glass to visualise that 4.  

26

 lies between 4.262 and 4.263.

Step 5: Divide the portion between 4.262 and 4.263 into  

10 equal parts and use a magnifying glass to visualise that 4.  

26

 lies between 4.2625 and 4.2627.

We note that 4.  

26

 is visualised closer to 4.263 than to 4.262.

The same procedure can be used to visualise a real number with a non-terminating and non-recurring decimal expansion on the number line to a required accuracy.

From the above discussions and visualisations we conclude again that every  

real number is represented by a unique point on the number line. Further every point on the number line represents one and only one real number.