Q.1. Visualise 3.765 on the number line, using successive magnification.
Ans. 3.765 lies between 3 and 4.
Let us divide the interval (3, 4) into 10 equal parts.
Since, 3.765 lies between 3.7 and 3.8. We again magnify the interval [3.7, 3.8] by dividing it further into 10 parts and concentrate the distance between 3.76 and 3.77.
The number 3.765 lies between 3.76 and 3.77. Therefore we further magnify the interval [3.76, 3.77] into 10 equal parts.
Now, the point corresponding to 3.765 is clearly located, as shown in Fig. (iii) above.
Q.2. Visualise on the number line, up to 4 decimal places.
Ans. Note: We can magnify an interval endlessly using successive magnification.
To visualize or 4.2626… on the number line up to 4 decimal places, we use the following steps.
I. The number 4.2626… lies between 4 and 5. Divide the interval [4, 5] in 10 smaller parts:
II. Obviously, the number 4.2626... lies between 4.2 and 4.3. We magnify the interval [4.2, 4.3]:
III. Next, we magnify the interval [4.26, 4.27]:
IV. Finally magnify the interval [4.262, 4.263]:
In Fig. (iv), we can easily observe the number 4.2626… or .