Chapter 2 Number System Ex 2.1

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 2 Number System Ex 2.1

Question 1.
Classify the following numbers as rational or irrational:
(i) √23
(ii) √225
(iii) 0.3796
(iv) 7.478478…
(v) 1.101001000100001…
Solution .
(i) √23
Here, 23 is not a perfect square number, hence, √23 is an irrational number.
(ii) √225
Here 225 is a perfect square of 15, hence √225 is a rational number.
(iii) 0.3796 can be written in  form,
where q ≠ 0 i.e 
Hence, it is a rational number.
(iv) 7.478478 i.e. 
Here, pair of digits (478) are repeating as it is non-terminating but recurring.
(v) 1.101001000100001…. is an irrational number is its decimal expansion is non-terminating and non-recurring.

Question 2.
Write three numbers whose decimal expansions are non-terminating non-recurring.
Solution.
The three numbers whose decimal expansions are non-terminating non-recurring i.e. irrational numbers are
0.01001000100001…..
0.02002000200002….
0.03003000300003…….. etc.

Question 3.
Write the following in decimal form and say what kind of decimal expansion each has:


Solution.

Question 4.
Express the following in the form , where p and q are integers and q ≠ 0.

Solution .
(i) Let x = 
i.e., x = 0.3333 …(i)
Multiplying (i) by 10, we get
10x = 3.3333 …(ii)
Subtracting (i) from (ii),
we get 10x – x = 3.3333… – 0.3333…

Question 5.
Find three different irrational numbers between the rational numbers  and .
Solution.

There are infinite irrational numbers between the two given numbers, we may choose any three of them, e.g.