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Exercise 1.4

1. Visualise 3.765 on the number line, using successive magnification.

Sol.
(i) We notice the number 3.7 lies between 3 and 4. So, first we locate numbers 3 and 4 on number line and divide the portion into ten equal parts and locate 3.7 and 3.8. [Refer step 2]
(ii) Further 3.76 lies between 3.7 and 3.8. So, we magnify 3.7 and 3.8 and divide the portion into ten equal parts and locate 3.76 and 3.77. [Refer step 3]
(iii) Further 3.765 lies between 3.76 and 3.77. So, we magnify 3.76 and 3.77 and divide the portion into ten equal parts and locate 3.765. [Refer step 4]

Point O in step 4 represents the number 3.765 on the number line.

2. Visualise $7.\overline {46}$ on the number line, up to 4 decimal places.

Sol. $4.\overline {26}$ = 4.2626262626………………….
Point O in step 5 represents the number $4.\overline {26}$ on the number line.