Class IX Math NCERT Solutions For Real Numbers Exercise– 1.4

Exercise– 1.4

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.

2.  Visualise 4.26 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, 4263]:

              

              In Fig. (iv), we can easily observe the number 4.2626. . . or