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Class 9 RD Sharma Solutions – Chapter 1 Number System – Exercise 1.2

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  • Last Updated : 03 Mar, 2021
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Question 1. Express the following rational numbers as decimals:

 i) 42/100

ii) 327/500

 iii) 15/4

Solutions:

(i) 42/100 

Using long division method:

So, 42/100 = 0.42

(ii) 327/500 

Using long division method:

So, 327/500 = 0.654

(iii) 15/4 

Using long division method:

So, 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 

(vi) 33/26

Solutions:

(i) Using long division method:  

So, 2/3 = 0.66.. = 0.\bar{6}

(ii) Using long division method:  

So, -4/9 = -0.44.. = -(0.\bar{4})

(iii) Using long division method:  

So, -2/15 = (- 0.133..) = (-0.1\bar{3})

(iv) -22/13 = -(1 + 9/13)

Using long division method:  

So, -22/3 = -(1.692307…) =  -(1.\overline{692307})

(v) 437/999 

Using long division method:  

   

So, 437/999 = 0.437… =  0.\overline{437}

(vi) 33/26 = 1\frac{7}{26}

Using long division method:  

So, 33/26 = 1.2692307… =  1.\overline{2692307}

Question 3. Look at several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy?

Solution:

p/q will be terminating decimal when prime factorization of q must have factors 2 or 5 or both.

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