RD Sharma 2020 solution class 9 chapter 1 Number System Exercise 1.3

Exercise 1.3

Page-1.22

Question 1:

Express each of the following decimals in the form $\frac{p}{q}:$

(i) 0.39
(ii) 0.750
(iii) 2.15
(iv) 7.010
(v) 9.90
(vi) 1.0001

Answer 1:

(i) Given decimal is

Now we have to convert given decimal number into the form

Let

Hence,

(ii) Given decimal is

Now we have to convert given decimal number into form

Let

Hence,

(iii) Given decimal is

Now we have to express the given decimal number into form

Let

Hence,

(iv) Given decimal is 7.010

Now we have to express the given decimal number into form

Let

Hence,

(v) Given decimal is

Now we have to find given decimal number into form

Let

Hence, =$\frac{99}{10}$

(vi) Given decimal is

Now we have to find given decimal number into form

Hence,

Question 2:

Express each of the following decimals in the form $\frac{p}{q}:$
(i) $0.\overline{4}$

(ii) $0.\overline{37}$

(iii) $0.\overline{54}$

(iv) $0.\overline{621}$

(v) $125.\overline{3}$

(vi) $4.\overline{7}$

(vii) $0.\overline{47}$

Answer 2:

(i) Let

Hence,

(ii) Let

Hence,

(iii) Let

Hence,

 

(iv) Let

Hence,

(v) Let

Hence,

(vi) Let

Let

Therefore,

Hence,

(vii) Let

Since,

Therefore,

Hence,