Question

Represent one terminating decimal with four decimal places on the number line using 'Succesive Magnification.​

Answer 1

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.

solution