Rajasthan Board RBSE Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.4 Textbook Exercise Questions and Answers.

## RBSE Class 9 Maths Solutions Chapter 1 Number Systems Exercise 1.4

Question 1.

Visualise 3.765 on the number line, using successive magnification.

Answer:

We know that 3.765 bes between 3 and 4. We divide the part of the number line between 3 and 4 into 10 equal parts and look at the portion between 3.7 and 3.8 through a magnifying glass and realize that, 3.765 lies between 3.7 and 3.8 [Fig. (i)]. Now, we imagine that part on the number line between 3.7 and 3.8] has been sub divided into 10 equal parts. As before, we can now visualize through the magnify glass that 3.765 lies in the portion between 3.76 and 3.77 [Fig. (ii)].

Now, we imagine that the portion between 3.76 and 3.77 has been sub divided into 10 equal parts [Fig. (iii)]. Here, we can visualise that 3.761 is the first mark and 3.765 is at the fifth mark. This process is known as the process of successive magnification.

Question 2.

Visualise \(4 . \overline{26}\) on the number line, up to 4 decimal places.

Answer:

We proceed by successive magnifications, and successively decrease the lengths of the portions on the number line in which, \(4 . \overline{26}\) is located. \(4 . \overline{26}\) is located in the portion between 4 and 5 of length 1. This portion is then divided into 10 equal parts [Fig. (i)]. We further locate \(4 . \overline{26}\) in the portion between 4.2 and 4.3 of length 0.1 [Fig. (ii)]. To get more accurate visualisation of the representation, we divide even this part into 10 equal parts and use a magnifying glass to visualise that \(4 . \overline{26}\) lies in the portion between 4.26 and 4.27 of length 0.01. To visualize \(4 . \overline{26}\) in

a portion of length 0.001, we again divide the new portion between 4.26 and 4.27 into 10 equal parts and visualise the representation of \(4 . \overline{26}\) in the portion between 4.262 and 4.263 of length 0.001 (Fig. (iii)]. Now, for a better visualisation, portion between 4.262 and 4.263 is further divided into 10 equal parts [Fig. (iv)]. \(4 . \overline{26}\) is located closer to 4.263 than to 4.262 at 4.2627.

We can proceed endlessly in this manner and simultaneously imagining the decrease in the length of the portion in which \(4 . \overline{26}\) is located.

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