RD Sharma Solutions Class 9 Number System Exercise 1.2

RD Sharma Solutions Class 9 Chapter 1 Ex 1.2

Q1. Express the following rational numbers as decimals:

(i) \(\frac{42}{100}\)

(ii) \(\frac{327}{500}\)

(iii) \(\frac{15}{4}\)

Solution:

(i) By long division method

100) \(\overline{42}\) ( 0.42

400

\(\overline{200}\)

200

\(\overline{0}\)

Therefore,  \(\frac{42}{100}\) = 0.42

(ii) By long division method

500) \(\overline{327.000}\) ( 0.654

3000

\(\overline{2700}\)

2500

\(\overline{2000}\)

2000

\(\overline{0}\)

Therefore,  \(\frac{327}{500}\) = 0.654

(iii) By long division method

4) \(\overline{15.00}\) ( 3.75

12

\(\overline{30}\)

28

\(\overline{20}\)

20

\(\overline{0}\)

Therefore,  \(\frac{15}{4}\) = 3.75

Q2. Express the following rational numbers as decimals:

(i) \(\frac{2}{3}\)

(ii) –\(\frac{4}{9}\)

(iii) –\(\frac{2}{15}\)

(iv) –\(\frac{22}{13}\)

(v)  \(\frac{437}{999}\)

Solution:

(i) By long division method

3) \(\overline{2.0000}\) ( 0.66

18

\(\overline{20}\)

18

\(\overline{2}\)

Therefore,  \(\frac{2}{3}\) = 0.66

(ii) By long division method

9) \(\overline{4.000}\) ( 0.444

3600

\(\overline{4000}\)

3600

\(\overline{4000}\)

3600

\(\overline{400}\)

Therefore, – \(\frac{4}{9}\) = – 0.444

(iii) By long division method

15) \(\overline{2.00}\) ( 1.333

15

\(\overline{50}\)

45

\(\overline{50}\)

45

\(\overline{50}\)

45

\(\overline{5}\)

Therefore,  \(\frac{2}{15}\) = -1.333

(iv) By long division method

13) \(\overline{22.000}\) ( 1.69230769

13

\(\overline{90}\)

78

\(\overline{120}\)

117

\(\overline{30}\)

26

\(\overline{40}\)

39

\(\overline{100}\)

91

\(\overline{90}\)

78

\(\overline{120}\)

117

\(\overline{3}\)

Therefore, – \(\frac{22}{13}\) = – 1.69230769

(v) By long division method

999) \(\overline{437.0000}\) ( 0.43743

3996

\(\overline{3740}\)

2997

\(\overline{7430}\)

6993

\(\overline{4370}\)

3996

\(\overline{3740}\)

2997

\(\overline{743}\)

Therefore,  \(\frac{437}{999}\) = 0.43743

Q3. Look at several examples of rational numbers in the form of

\(\frac{p}{q}\) (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 \(\frac{p}{q}\) is a terminating decimal

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

\(\frac{p}{q}\)   is a terminating decimal only, when prime

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