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```Chapter 1: Number System Exercise – 1.2

Question: 1

Express the following rational numbers as decimals:

(i) 42/100

(ii) 327/500

(iii) 15/4

Solution:

(i) By long division method Therefore, 42/100 = 0.42

(ii) By long division method Therefore, 327/500 = 0.654

(iii) By long division method Therefore, 15/4 = 3.75

Question: 2

Express the following rational numbers as decimals:

(i)  2/3

(ii) – (4/9)

(iii) – (2/15)

(iv) – (22/13)

(v)   437/999

Solution:

(i) By long division method Therefore, 2/3 = 0.66

(ii) By long division method Therefore, - 4/9 = - 0.444

(iii) By long division method Therefore, 2/15 = -1.333

(iv) By long division method Therefore, - 22/13 = - 1.69230769

(v) By long division method Therefore, 437/999 = 0.43743

Question: 3

Look at several examples of rational numbers in the form of p/q (q ≠ 0), where p and q are integers with no common factor other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?

Solution:

A rational number p/q is a terminating decimal

only, when prime factors of q are q and 5 only. Therefore,

p/q is a terminating decimal only, when prime

factorization of q must have only powers of 2 or 5 or both.
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